diff --git a/examples/causal_inference/assurance_planning_simulation.ipynb b/examples/causal_inference/assurance_planning_simulation.ipynb new file mode 100644 index 000000000..260a38c65 --- /dev/null +++ b/examples/causal_inference/assurance_planning_simulation.ipynb @@ -0,0 +1,1756 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0e1fc447", + "metadata": {}, + "source": [ + "(assurance_planning)=\n", + "# Assurance Planning via Simulation\n", + "\n", + ":::{post} May 2026\n", + ":tags: experimentation, decision analysis, power analysis, assurance, simulation\n", + ":category: intermediate, reference\n", + ":author: Nathaniel Forde\n", + ":::\n", + "\n", + ":::{figure} experimentation_triptych.jpeg\n", + ":name: experimentation-triptych\n", + ":width: 100%\n", + ":align: center\n", + "\n", + "The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance (this notebook):* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis:* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis:* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery.\n", + ":::\n", + "\n", + "Experimental questions are seeded in the science that preceded them. Answers are stress-tested and refined. New experiments spawn further questions again. This is the cycle. \n", + "\n", + "## The question planners are actually asking\n", + "\n", + "When we experiment, we encode questions. Implicitly we assume an answer will be useful. Our hypotheses are \"operationalised\" as power heuristics: given an effect size, what is the probability we cross a fixed threshold? This is an indirect and contorted gauge of efficacy. Instead of asking whether the treatment is effective, we often ask whether the results are surprising assuming a degree of effectiveness. The slippage between these two questions has produced a generation of experimental plans calibrated to invented effect sizes rather than to the beliefs the planners actually hold.\n", + "\n", + "An alternative is Bayesian Assurance. The construction is mechanical: draw from the priors, generate a dataset, fit the treatment model, apply the decision rule, repeat. The result is a single number: the probability the experiment will conclude what its stakeholders need. The process is the same whether the response is continuous (like revenue per visitor) or binary (like conversion); we develop it on the Gaussian case first and confirm the process is invariant to the response scale. This notebook is the first of three on the lifecycle of a Bayesian experiment; see {ref}`sensitivity_confounding` for the interpretation counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The same inferential machinery serves all three panels of the triptych, but what changes is the problem put to it.\n", + "\n", + ":::{admonition} Where this lands in regulatory practice\n", + ":class: note\n", + "\n", + "We are going to apply Bayesian assurance to a question in product-analytics but the technique has a wider application. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials defines *Bayesian power* as the probability of meeting the success criterion averaged over a prior distribution {cite:p}`fda2026bayesian`, which is assurance under another name. The FDA guidance formalises the success rule as $\\Pr(\\text{effect} > a) > c$ (the rule used below, with $a = 0$ and $c = 0.95$). The same guidance separates the *design prior* that generates the synthetic trials from the *analysis prior* used in inference. The generative and inference models below are distinct objects for this reason. Below we'll runs the assurance loop with the two priors deliberately mismatched. The clinical trial setting in the FDA report differs from product experimentation; the machinery is identical.\n", + ":::" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1d31774d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:15:59.450449Z", + "iopub.status.busy": "2026-06-01T17:15:59.450345Z", + "iopub.status.idle": "2026-06-01T17:16:02.392965Z", + "shell.execute_reply": "2026-06-01T17:16:02.392082Z" + } + }, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "from dataclasses import dataclass\n", + "\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.ticker as mticker\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pymc as pm\n", + "\n", + "from scipy import stats\n", + "\n", + "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", + "warnings.filterwarnings(\"ignore\", category=UserWarning)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7b97cc23", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:02.394961Z", + "iopub.status.busy": "2026-06-01T17:16:02.394718Z", + "iopub.status.idle": "2026-06-01T17:16:02.734659Z", + "shell.execute_reply": "2026-06-01T17:16:02.733931Z" + } + }, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = 'retina'\n", + "az.style.use(\"arviz-variat\")\n", + "rng = np.random.default_rng(42)\n", + "RANDOM_SEED = 42" + ] + }, + { + "cell_type": "markdown", + "id": "565c8ac0", + "metadata": {}, + "source": [ + "### The scenario\n", + "\n", + "An e-commerce team is evaluating a redesigned checkout flow. We cover two outcomes: the continuous outcome is revenue per visitor, the binary outcome is conversion. We will not commit to a particular vertical or product; the structure is generic to any A/B test with one of these outcome types. What matters is that the same prior beliefs and the same decision rule will be asked of two different likelihoods. The Gaussian case will carry the argument; the Bernoulli case will confirm it travels." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "85d2d6a4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:02.736865Z", + "iopub.status.busy": "2026-06-01T17:16:02.736627Z", + "iopub.status.idle": "2026-06-01T17:16:02.739489Z", + "shell.execute_reply": "2026-06-01T17:16:02.738866Z" + } + }, + "outputs": [], + "source": [ + "@dataclass\n", + "class EffectPrior:\n", + " \"\"\"Prior beliefs about a treatment effect, on the scale of the outcome.\"\"\"\n", + "\n", + " mu: float\n", + " sigma: float\n", + "\n", + " def sample(self, rng, size=1):\n", + " return rng.normal(self.mu, self.sigma, size=size)" + ] + }, + { + "cell_type": "markdown", + "id": "541c0d41", + "metadata": {}, + "source": [ + "## Power and assurance: two questions, different focus\n", + "\n", + "Power and assurance share an interface and answer different questions. Power conditions on a specific effect size $\\theta_0$ that the planner has been pressed into naming, and computes the probability of rejecting the null at that value:\n", + "\n", + "$$\n", + "\\text{Power}(N) = P\\!\\left(\\text{reject } H_0 \\mid \\theta = \\theta_0,\\; N\\right).\n", + "$$\n", + "\n", + "The conditioning bar is the load-bearing part. The planner who has confidently named $\\theta_0$ has implicitly used up the uncertainty that motivated the experiment in the first place. Assurance refuses the substitution. Instead it integrates over the planner's prior beliefs about the effect. The decision rule is whether the posterior probability of a positive effect clears a threshold $c$:\n", + "\n", + "$$\n", + "\\text{Assurance}(N) = \\mathbb{E}_{\\substack{\\theta \\,\\sim\\, \\pi(\\theta) \\\\ \\hat{d} \\,\\sim\\, p(\\hat{d} \\mid \\theta,\\, N)}}\\!\\left[\\mathbb{1}\\!\\bigl(P(\\theta > 0 \\mid \\hat{d},\\, N) > c\\bigr)\\right].\n", + "$$\n", + "\n", + "The outer expectation averages over effect sizes drawn from the prior; the inner averages over data generated under each effect ({cite:p}`ohagan2005assurance`, {cite:p}`spiegelhalter2004bayesian`). The integration is the entire move. Where power asks the planner to invent a world, assurance asks them to describe the one they already believe they are in. With that description in place, we can quantify how likely the result is when conditioned on the prior distribution. \n", + "\n", + "## The simulation engine\n", + "\n", + "Assurance is an expectation over the *prior predictive distribution*: the joint distribution of effect and data that the model generates before any real data arrive. As a Monte Carlo estimator the integral becomes a procedure in three steps, repeated for each candidate sample size:\n", + "\n", + "1. **Sample the prior predictive** of an unconditioned generative model. Each draw is a complete synthetic experiment: an effect drawn from the prior, and a dataset of size $N$ generated under it.\n", + "2. **Fit the analysis model** to each synthetic dataset and apply the decision rule.\n", + "3. **Record** the fraction of synthetic experiments in which the decision succeeded.\n", + "\n", + "Drawing a truth and generating data under it is exactly what `pm.sample_prior_predictive` does on a model with no observed data, so we let PyMC's generative machinery produce the synthetic experiments rather than hand-rolling the sampling with `numpy`. The generative model that produces the data and the inference model that analyses it are separate objects, and keeping them separate is the point: the generative model encodes the worlds we are planning for, the inference model encodes how we will reason once real data arrive. This workflow is defined as a function and passed through a sample size grid to determine how many _N_ is required to achieve surety in the finding. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "8f2c40f5", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:02.741148Z", + "iopub.status.busy": "2026-06-01T17:16:02.741022Z", + "iopub.status.idle": "2026-06-01T17:16:02.743743Z", + "shell.execute_reply": "2026-06-01T17:16:02.743193Z" + } + }, + "outputs": [], + "source": [ + "def assurance_curve(assurance_fn, N_grid, n_sims, rng, **kwargs):\n", + " \"\"\"Estimate the assurance curve by evaluating assurance at each sample size.\"\"\"\n", + " records = []\n", + " for N in N_grid:\n", + " a = assurance_fn(N=int(N), n_sims=n_sims, rng=rng, **kwargs)\n", + " records.append({\"N\": int(N), \"assurance\": a})\n", + " return pd.DataFrame(records)" + ] + }, + { + "cell_type": "markdown", + "id": "3f49b072", + "metadata": {}, + "source": [ + "## Gaussian outcome: revenue per visitor\n", + "\n", + "The Gaussian case is the cleanest place to make the mechanics explicit. Each arm produces a revenue-per-visitor outcome with known noise scale $\\sigma_{\\text{obs}}$ (we treat this as known here; in practice it is estimated from a pilot or historical data). The team is interested in the treatment effect $\\delta = \\mu_B - \\mu_A$, and holds a prior over $\\delta$ informed by past experiments in similar product surfaces. That prior is not conjured from nothing: {ref}`meta_analysis_experiments` shows how a meta-analysis of past experiments produces exactly this kind of prior, so the synthesis at the end of one experiment's lifecycle is the planning input at the start of the next. Concretely, the meta-analytic predictive there closes on $\\mathcal{N}(0.4, 0.5)$, which is exactly the `EFFECT_PRIOR` defined below: the number that ends that notebook opens this one.\n", + "\n", + "Two models do the work. The *generative model* is unconditioned: it places the planning prior on $\\delta$ and generates synthetic datasets, and it is the object we hand to `pm.sample_prior_predictive`. The *inference model* conditions on a dataset and returns the posterior on $\\delta$; the decision rule asks whether the posterior probability of a positive effect exceeds a threshold (0.95 below). For the assurance loop the conjugate Normal–Normal posterior on $\\delta$ admits a closed form, which lets us evaluate the decision on each synthetic experiment without running MCMC every time. \n", + "\n", + "We will verify that closed form against the inference model's MCMC posterior at a single sample size before relying on it. This also underwrites the idea that we can use MCMC for this procedure even with more complex models. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4f485b3b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:02.744949Z", + "iopub.status.busy": "2026-06-01T17:16:02.744852Z", + "iopub.status.idle": "2026-06-01T17:16:02.748080Z", + "shell.execute_reply": "2026-06-01T17:16:02.747587Z" + } + }, + "outputs": [], + "source": [ + "SIGMA_OBS = 4.0\n", + "DECISION_THRESHOLD = 0.95\n", + "BASELINE_REVENUE = 10.0\n", + "# Not free-floating: this is the meta-analytic predictive for a new market from\n", + "# the synthesis notebook (meta_analysis_experiments), which closes on N(0.4, 0.5).\n", + "EFFECT_PRIOR = EffectPrior(mu=0.4, sigma=0.5)\n", + "\n", + "\n", + "def gaussian_generative_model(N, prior):\n", + " \"\"\"Unconditioned model: planning prior on the effect plus the data-generating likelihood.\"\"\"\n", + " with pm.Model() as model:\n", + " delta = pm.Normal(\"delta\", mu=prior.mu, sigma=prior.sigma)\n", + " pm.Normal(\"y_A\", mu=BASELINE_REVENUE, sigma=SIGMA_OBS, shape=N)\n", + " pm.Normal(\"y_B\", mu=BASELINE_REVENUE + delta, sigma=SIGMA_OBS, shape=N)\n", + " return model\n", + "\n", + "\n", + "def gaussian_two_arm_model(y_A, y_B, prior):\n", + " \"\"\"Inference model: conditions on an observed dataset and returns the posterior on the effect.\"\"\"\n", + " with pm.Model() as model:\n", + " mu_A = pm.Normal(\"mu_A\", mu=BASELINE_REVENUE, sigma=5.0)\n", + " delta = pm.Normal(\"delta\", mu=prior.mu, sigma=prior.sigma)\n", + " mu_B = pm.Deterministic(\"mu_B\", mu_A + delta)\n", + " pm.Normal(\"obs_A\", mu=mu_A, sigma=SIGMA_OBS, observed=y_A)\n", + " pm.Normal(\"obs_B\", mu=mu_B, sigma=SIGMA_OBS, observed=y_B)\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "be971533", + "metadata": {}, + "source": [ + "A single synthetic experiment makes the inference model concrete. We use the do-operator to fix the generative effect at a chosen value, draw one dataset from the prior predictive, and condition the inference model on it." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "0a894159", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:02.749699Z", + "iopub.status.busy": "2026-06-01T17:16:02.749608Z", + "iopub.status.idle": "2026-06-01T17:16:05.230742Z", + "shell.execute_reply": "2026-06-01T17:16:05.230108Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [y_A, y_B]\n", + "NUTS[nutpie]: [mu_A, delta]\n" + ] + } + ], + "source": [ + "demo_true_delta = 0.6\n", + "demo_model = pm.do(gaussian_generative_model(N=200, prior=EFFECT_PRIOR), {\"delta\": demo_true_delta})\n", + "demo_draw = pm.sample_prior_predictive(1, model=demo_model, random_seed=RANDOM_SEED)\n", + "y_A_demo = demo_draw.prior[\"y_A\"].values.reshape(-1)\n", + "y_B_demo = demo_draw.prior[\"y_B\"].values.reshape(-1)\n", + "\n", + "with gaussian_two_arm_model(y_A_demo, y_B_demo, EFFECT_PRIOR):\n", + " idata_gauss_demo = pm.sample(\n", + " draws=1000,\n", + " tune=1000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0b654f32", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:05.232117Z", + "iopub.status.busy": "2026-06-01T17:16:05.232021Z", + "iopub.status.idle": "2026-06-01T17:16:06.028378Z", + "shell.execute_reply": "2026-06-01T17:16:06.027943Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1445 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "pc = az.plot_dist(\n", + " idata_gauss_demo,\n", + " var_names=[\"delta\"],\n", + " visuals={\"title\": {\"text\": r\"Posterior on $\\delta$ at $N=200$ (one simulated dataset)\"}},\n", + ")\n", + "az.add_lines(\n", + " pc,\n", + " values=0.0,\n", + " visuals={\"ref_line\": {\"color\": \"C1\", \"label\": \"ref = 0.0\"}},\n", + ")\n", + "pc.get_viz(\"plot\").legend();" + ] + }, + { + "cell_type": "markdown", + "id": "3f515a2e", + "metadata": {}, + "source": [ + "The posterior concentrates above zero; under the decision rule the team would conclude the new flow lifts revenue. That is a single draw of the experiment. Assurance asks how often this conclusion would arrive if we re-ran the experiment many times under our actual prior.\n", + "\n", + "The conjugate posterior on $\\delta$ given $\\hat d = \\bar y_B - \\bar y_A$ has mean and variance:\n", + "\n", + "$$\n", + "\\sigma_d^2 = \\frac{2\\sigma_{\\text{obs}}^2}{N}, \\quad\n", + "\\tau^2_{\\text{post}} = \\left(\\frac{1}{\\tau_0^2} + \\frac{1}{\\sigma_d^2}\\right)^{-1}, \\quad\n", + "\\mu_{\\text{post}} = \\tau^2_{\\text{post}}\\left(\\frac{\\mu_0}{\\tau_0^2} + \\frac{\\hat d}{\\sigma_d^2}\\right),\n", + "$$\n", + "\n", + "where $(\\mu_0, \\tau_0)$ is the prior on $\\delta$. We check this matches the PyMC posterior before relying on it." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "42e775d9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:06.029977Z", + "iopub.status.busy": "2026-06-01T17:16:06.029758Z", + "iopub.status.idle": "2026-06-01T17:16:06.037195Z", + "shell.execute_reply": "2026-06-01T17:16:06.036727Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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analyticalMCMC
posterior mean of delta0.7450.728
posterior sd of delta0.3120.303
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" + ], + "text/plain": [ + " analytical MCMC\n", + "posterior mean of delta 0.745 0.728\n", + "posterior sd of delta 0.312 0.303" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def gaussian_posterior_delta(d_hat, N, sigma_obs, prior):\n", + " sigma_d_sq = 2 * sigma_obs**2 / N\n", + " post_var = 1.0 / (1.0 / prior.sigma**2 + 1.0 / sigma_d_sq)\n", + " post_mean = post_var * (prior.mu / prior.sigma**2 + d_hat / sigma_d_sq)\n", + " return post_mean, np.sqrt(post_var)\n", + "\n", + "\n", + "d_hat_demo = y_B_demo.mean() - y_A_demo.mean()\n", + "analytical_mu, analytical_sd = gaussian_posterior_delta(\n", + " d_hat_demo, N=200, sigma_obs=SIGMA_OBS, prior=EFFECT_PRIOR\n", + ")\n", + "mcmc_mu = idata_gauss_demo.posterior[\"delta\"].mean().item()\n", + "mcmc_sd = idata_gauss_demo.posterior[\"delta\"].std().item()\n", + "\n", + "pd.DataFrame(\n", + " {\"analytical\": [analytical_mu, analytical_sd], \"MCMC\": [mcmc_mu, mcmc_sd]},\n", + " index=[\"posterior mean of delta\", \"posterior sd of delta\"],\n", + ").round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "fb2d9901", + "metadata": {}, + "source": [ + "The two posteriors agree to within MCMC noise. Now we get to the heart of the technique and push our procedure through different sample values of _N_." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "62b0f123", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:06.038338Z", + "iopub.status.busy": "2026-06-01T17:16:06.038265Z", + "iopub.status.idle": "2026-06-01T17:16:08.642660Z", + "shell.execute_reply": "2026-06-01T17:16:08.642201Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n" + ] + }, + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " N assurance\n", + "0 100 0.267\n", + "1 200 0.398\n", + "2 400 0.501\n", + "3 800 0.603\n", + "4 1600 0.640\n", + "5 3200 0.681\n", + "6 6400 0.717" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def gaussian_assurance_at_N(N, n_sims, prior, sigma_obs, threshold, rng, analysis_prior=None):\n", + " # `prior` is the design prior: it generates the synthetic worlds. `analysis_prior`\n", + " # is used to form the posterior; it defaults to the design prior so a single\n", + " # argument reproduces the matched-prior case.\n", + " analysis_prior = prior if analysis_prior is None else analysis_prior\n", + " seed = int(rng.integers(2**31 - 1))\n", + " pp = pm.sample_prior_predictive(\n", + " n_sims, model=gaussian_generative_model(N, prior), random_seed=seed\n", + " )\n", + " y_A = pp.prior[\"y_A\"].values.reshape(n_sims, N)\n", + " y_B = pp.prior[\"y_B\"].values.reshape(n_sims, N)\n", + " d_hat = y_B.mean(axis=1) - y_A.mean(axis=1)\n", + " post_mu, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, analysis_prior)\n", + " prob_positive = 1.0 - stats.norm.cdf(0.0, loc=post_mu, scale=post_sd)\n", + " return float((prob_positive > threshold).mean())\n", + "\n", + "\n", + "N_GRID = np.array([100, 200, 400, 800, 1600, 3200, 6400])\n", + "N_SIMS = 1000\n", + "\n", + "assurance_df = assurance_curve(\n", + " gaussian_assurance_at_N,\n", + " N_grid=N_GRID,\n", + " n_sims=N_SIMS,\n", + " rng=np.random.default_rng(RANDOM_SEED),\n", + " prior=EFFECT_PRIOR,\n", + " sigma_obs=SIGMA_OBS,\n", + " threshold=DECISION_THRESHOLD,\n", + ")\n", + "assurance_df" + ] + }, + { + "cell_type": "markdown", + "id": "191f92bd", + "metadata": {}, + "source": [ + "For each simulated future dataset, we compute the posterior distribution of the treatment effect and evaluate the posterior probability that the effect is positive, `prob_positive`. A trial is considered decisive if `prob_positive` exceeds the pre-specified `DECISION_THRESHOLD`. The Bayesian assurance is the proportion of simulated trials that satisfy this decision criterion. As the planned sample size increases, posterior uncertainty decreases, leading to a larger proportion of decisive trials and therefore higher assurance.\n", + "\n", + "For comparison we compute frequentist power at a single fixed effect size. The convention is to set the effect to the prior mean, which is itself an arbitrary choice, and a revealing one." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "87ca67e9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:08.644059Z", + "iopub.status.busy": "2026-06-01T17:16:08.643954Z", + "iopub.status.idle": "2026-06-01T17:16:08.957767Z", + "shell.execute_reply": "2026-06-01T17:16:08.957314Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 1123, + "width": 3023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_power(N, delta_alt, sigma_obs, alpha=0.05):\n", + " sigma_d = np.sqrt(2 * sigma_obs**2 / N)\n", + " z_crit = stats.norm.ppf(1 - alpha)\n", + " return 1.0 - stats.norm.cdf(z_crit - delta_alt / sigma_d)\n", + "\n", + "\n", + "power_at_prior_mean = np.array([gaussian_power(N, EFFECT_PRIOR.mu, SIGMA_OBS) for N in N_GRID])\n", + "power_at_optimistic = np.array(\n", + " [gaussian_power(N, EFFECT_PRIOR.mu + EFFECT_PRIOR.sigma, SIGMA_OBS) for N in N_GRID]\n", + ")\n", + "power_at_pessimistic = np.array(\n", + " [gaussian_power(N, max(EFFECT_PRIOR.mu - EFFECT_PRIOR.sigma, 0.01), SIGMA_OBS) for N in N_GRID]\n", + ")\n", + "\n", + "prior_prob_positive = 1.0 - stats.norm.cdf(0.0, EFFECT_PRIOR.mu, EFFECT_PRIOR.sigma)\n", + "\n", + "fig, ax = plt.subplots(figsize=(15, 5.5))\n", + "ax.plot(N_GRID, assurance_df[\"assurance\"], marker=\"o\", linewidth=2, label=\"Assurance (Bayesian)\")\n", + "ax.plot(\n", + " N_GRID,\n", + " power_at_prior_mean,\n", + " marker=\"s\",\n", + " linestyle=\"--\",\n", + " label=r\"Power at $\\theta_0 = \\mu_{\\text{prior}}$\",\n", + ")\n", + "ax.plot(\n", + " N_GRID,\n", + " power_at_optimistic,\n", + " marker=\"^\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=r\"Power at $\\mu + \\sigma$\",\n", + ")\n", + "ax.plot(\n", + " N_GRID,\n", + " power_at_pessimistic,\n", + " marker=\"v\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=r\"Power at $\\mu - \\sigma$\",\n", + ")\n", + "ax.axhline(\n", + " prior_prob_positive,\n", + " color=\"C0\",\n", + " linestyle=\"-.\",\n", + " alpha=0.6,\n", + " label=rf\"Assurance ceiling $P(\\delta>0)$ = {prior_prob_positive:.2f}\",\n", + ")\n", + "ax.set_xscale(\"log\")\n", + "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n", + "ax.set_xlabel(\"Sample size per arm\")\n", + "ax.set_ylabel(\"Probability of declaring uplift\")\n", + "ax.set_title(\"Assurance vs frequentist power, Gaussian outcome\")\n", + "ax.legend(loc=\"lower right\", fontsize=9);" + ] + }, + { + "cell_type": "markdown", + "id": "45105766", + "metadata": {}, + "source": [ + "The three power curves fan out because each conditions on a single assumed world. Power at $\\mu + \\sigma$ assumes an effect of $0.9$ and saturates almost immediately; power at $\\mu - \\sigma$ is pinned near the test's five-percent floor, because $\\mu - \\sigma$ lands at essentially zero effect, where even large samples gain almost no detection. Power at the prior mean is the curve a frequentist planner would actually quote. The assurance curve is the prior-weighted integral across the entire fan, and it tells a different story than any single power calculation.\n", + "\n", + "The story is in the crossing. Between $N=400$ and $N=800$ the assurance curve drops below power-at-the-mean, having sat above it at smaller samples. At small samples assurance is buoyed by the optimistic tail of the prior: it counts the plausible draws above $0.4$, effects of $0.8$ or $1.0$ that even a hundred observations have a real chance of detecting, which the single-point power calculation never sees. Quoting power at the mean understates what small experiments can do, because it ignores the optimistic tail of the prior that assurance counts.\n", + "\n", + "At large samples the relationship inverts, and the reason is the ceiling drawn above. Power at a fixed positive effect climbs to one: with enough data an effect of $0.4$ is certain to be detected. Assurance cannot reach one: the prior assigns positive probability to a zero or negative effect. Its asymptote is exactly the prior probability that the effect is beneficial, $P(\\delta > 0) \\approx 0.79$. No sample size buys more assurance than $P(\\delta > 0)$. A planner should know that ceiling before committing to more data, and no point on a power curve reveals it.\n", + "\n", + ":::{admonition} The minimum detectable effect leads a double life\n", + ":class: note\n", + "\n", + "Power is usually quoted at a \"minimum detectable effect\" (MDE), and that single number carries more weight than it appears to. Read one way, the MDE is a *utility threshold*: an effect smaller than this is not worth shipping, so failing to detect it does not matter, and powering at the MDE is a coherent design target. Read another way, it is a *forecast*: a quiet assumption that the true effect is about this large and positive, sometimes reverse-engineered from the sample size a team can already afford. The frequentist machinery itself is innocent here, because the false-positive rate $\\alpha$ already governs the null case; it is the floor that the $\\mu - \\sigma$ curve traces. What conditions the null away is the reported summary, \"$X\\%$ power to detect the MDE\", which is computed entirely inside the world where the effect is real and exactly the MDE. Assurance does not abolish this assumption. It relocates it from an implicit point to an explicit prior, where the probability that the effect is null or harmful becomes visible and open to argument.\n", + ":::\n", + "\n", + "## The same machinery on a binary outcome\n", + "\n", + "The generative model fixes the baseline conversion rate, places the planning prior on the lift, and emits binomial counts per arm. The inference step places Beta priors on the per-arm rates and reads off the posterior probability that the lift is positive ({cite:p}`stucchio2015bayesian`, {cite:p}`kruschke2014doing`)." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "d1c18825", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:08.959292Z", + "iopub.status.busy": "2026-06-01T17:16:08.959195Z", + "iopub.status.idle": "2026-06-01T17:16:08.963301Z", + "shell.execute_reply": "2026-06-01T17:16:08.962866Z" + } + }, + "outputs": [], + "source": [ + "BASELINE_RATE = 0.10\n", + "RATE_LIFT_PRIOR = EffectPrior(mu=0.005, sigma=0.012)\n", + "BETA_PRIOR_KAPPA = 200 # prior concentration, in units of pseudo-observations\n", + "prior_prob_lift_positive = 1.0 - stats.norm.cdf(0.0, RATE_LIFT_PRIOR.mu, RATE_LIFT_PRIOR.sigma)\n", + "\n", + "\n", + "def beta_prior_params(p_mean, kappa):\n", + " return kappa * p_mean, kappa * (1 - p_mean)\n", + "\n", + "\n", + "def bernoulli_generative_model(N, rate_prior, baseline_rate):\n", + " \"\"\"Unconditioned model: fixed baseline rate, planning prior on the lift, binomial counts per arm.\"\"\"\n", + " with pm.Model() as model:\n", + " lift = pm.Normal(\"lift\", mu=rate_prior.mu, sigma=rate_prior.sigma)\n", + " p_B = pm.Deterministic(\"p_B\", pm.math.clip(baseline_rate + lift, 1e-4, 1 - 1e-4))\n", + " pm.Binomial(\"n_A\", n=N, p=baseline_rate)\n", + " pm.Binomial(\"n_B\", n=N, p=p_B)\n", + " return model\n", + "\n", + "\n", + "def bernoulli_assurance_at_N(\n", + " N, n_sims, rate_prior, baseline_rate, kappa, threshold, rng, n_post=2000\n", + "):\n", + " seed = int(rng.integers(2**31 - 1))\n", + " pp = pm.sample_prior_predictive(\n", + " n_sims,\n", + " model=bernoulli_generative_model(N, rate_prior, baseline_rate),\n", + " random_seed=seed,\n", + " )\n", + " n_A = pp.prior[\"n_A\"].values.reshape(-1).astype(int)\n", + " n_B = pp.prior[\"n_B\"].values.reshape(-1).astype(int)\n", + " actual_sims = len(n_A) # PyMC v6 may return fewer draws than requested\n", + " alpha0, beta0 = beta_prior_params(baseline_rate, kappa)\n", + " p_A_post = rng.beta(alpha0 + n_A[:, None], beta0 + N - n_A[:, None], size=(actual_sims, n_post))\n", + " p_B_post = rng.beta(alpha0 + n_B[:, None], beta0 + N - n_B[:, None], size=(actual_sims, n_post))\n", + " prob_positive = (p_B_post > p_A_post).mean(axis=1)\n", + " return float((prob_positive > threshold).mean())" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "bc3152a4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:08.964993Z", + "iopub.status.busy": "2026-06-01T17:16:08.964890Z", + "iopub.status.idle": "2026-06-01T17:16:13.436502Z", + "shell.execute_reply": "2026-06-01T17:16:13.436021Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n", + "Sampling: [lift, n_A, n_B]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 923, + "width": 3023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "N_GRID_BERN = np.array([500, 1000, 2000, 4000, 8000, 16000, 32000])\n", + "\n", + "assurance_bern_df = assurance_curve(\n", + " bernoulli_assurance_at_N,\n", + " N_grid=N_GRID_BERN,\n", + " n_sims=N_SIMS,\n", + " rng=np.random.default_rng(RANDOM_SEED),\n", + " rate_prior=RATE_LIFT_PRIOR,\n", + " baseline_rate=BASELINE_RATE,\n", + " kappa=BETA_PRIOR_KAPPA,\n", + " threshold=DECISION_THRESHOLD,\n", + ")\n", + "\n", + "\n", + "def bernoulli_power(N, p_A, lift_alt, alpha=0.05):\n", + " p_B = p_A + lift_alt\n", + " p_bar = 0.5 * (p_A + p_B)\n", + " se_null = np.sqrt(2 * p_bar * (1 - p_bar) / N)\n", + " se_alt = np.sqrt(p_A * (1 - p_A) / N + p_B * (1 - p_B) / N)\n", + " z_crit = stats.norm.ppf(1 - alpha)\n", + " return 1.0 - stats.norm.cdf((z_crit * se_null - lift_alt) / se_alt)\n", + "\n", + "\n", + "power_bern_at_prior_mean = np.array(\n", + " [bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu) for N in N_GRID_BERN]\n", + ")\n", + "power_bern_at_optimistic = np.array(\n", + " [\n", + " bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu + RATE_LIFT_PRIOR.sigma)\n", + " for N in N_GRID_BERN\n", + " ]\n", + ")\n", + "power_bern_at_pessimistic = np.array(\n", + " [\n", + " bernoulli_power(N, BASELINE_RATE, max(RATE_LIFT_PRIOR.mu - RATE_LIFT_PRIOR.sigma, 1e-4))\n", + " for N in N_GRID_BERN\n", + " ]\n", + ")\n", + "\n", + "fig, ax = plt.subplots(figsize=(15, 4.5))\n", + "ax.plot(\n", + " N_GRID_BERN,\n", + " assurance_bern_df[\"assurance\"],\n", + " marker=\"o\",\n", + " linewidth=2,\n", + " label=\"Assurance (Bayesian)\",\n", + ")\n", + "ax.plot(\n", + " N_GRID_BERN,\n", + " power_bern_at_prior_mean,\n", + " marker=\"s\",\n", + " linestyle=\"--\",\n", + " label=r\"Power at lift $=\\mu_{\\text{prior}}$\",\n", + ")\n", + "ax.plot(\n", + " N_GRID_BERN,\n", + " power_bern_at_optimistic,\n", + " marker=\"^\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=r\"Power at $\\mu + \\sigma$\",\n", + ")\n", + "ax.plot(\n", + " N_GRID_BERN,\n", + " power_bern_at_pessimistic,\n", + " marker=\"v\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=r\"Power at $\\mu - \\sigma$\",\n", + ")\n", + "ax.axhline(\n", + " prior_prob_lift_positive,\n", + " color=\"C0\",\n", + " linestyle=\"-.\",\n", + " alpha=0.6,\n", + " label=rf\"Assurance ceiling $P(\\text{{lift}}>0)$ = {prior_prob_lift_positive:.2f}\",\n", + ")\n", + "\n", + "ax.set_xscale(\"log\")\n", + "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n", + "ax.set_xlabel(\"Sample size per arm\")\n", + "ax.set_ylabel(\"Probability of declaring uplift\")\n", + "ax.set_title(\"Assurance vs frequentist power, Bernoulli outcome\")\n", + "ax.legend(loc=\"lower right\");" + ] + }, + { + "cell_type": "markdown", + "id": "45306fae", + "metadata": {}, + "source": [ + "The conversion-rate version runs the same loop, and the loop discloses something the Gaussian case conceals. The lift is bounded above: how large a positive effect can even be depends on how much room sits above the baseline conversion rate, a constraint the Normal likelihood never faces. The Beta prior on the per-arm rates is parameterised here by a concentration $\\kappa$, the number of pseudo-observations at the baseline rate that the prior is equivalent to. Setting $\\kappa = 200$ is saying: I am as confident about the baseline as if I had watched 200 trials at that rate. This is a different handle on prior calibration than the Normal's mean and standard deviation pair, and it makes the ceiling claim more precise: the assurance curve asymptotes toward the prior probability that the lift is positive, and what that probability is depends not only on the prior's location and scale but on the scale on which the lift is defined. At a 10\\% baseline with a planning prior mean of 0.5\\%, the prior splits its mass roughly two to one in favour of a positive lift, and the assurance curve asymptotes there, near 0.66. The same machinery produces a lower ceiling than the Gaussian case because the planning prior commits to a more cautious belief about how large a conversion lift can plausibly be. The generative model produced the synthetic experiments; the conjugate Beta posterior supplied the decision, with no MCMC in the loop. We confirm below that this matches a full PyMC fit on a single dataset, so nothing in the assurance machinery depends on the closed form being available; it depends only on a posterior we can compute reliably." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "67f5d44e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:13.438114Z", + "iopub.status.busy": "2026-06-01T17:16:13.438020Z", + "iopub.status.idle": "2026-06-01T17:16:16.115505Z", + "shell.execute_reply": "2026-06-01T17:16:16.115030Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [n_A, n_B]\n", + "NUTS[nutpie]: [p_A, p_B]\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1223 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "def bernoulli_two_arm_model(n_A, n_B, N, baseline_rate, kappa):\n", + " alpha0, beta0 = beta_prior_params(baseline_rate, kappa)\n", + " with pm.Model() as model:\n", + " p_A = pm.Beta(\"p_A\", alpha=alpha0, beta=beta0)\n", + " p_B = pm.Beta(\"p_B\", alpha=alpha0, beta=beta0)\n", + " pm.Deterministic(\"lift\", p_B - p_A)\n", + " pm.Binomial(\"obs_A\", n=N, p=p_A, observed=n_A)\n", + " pm.Binomial(\"obs_B\", n=N, p=p_B, observed=n_B)\n", + " return model\n", + "\n", + "\n", + "demo_model_bern = pm.do(\n", + " bernoulli_generative_model(N=4000, rate_prior=RATE_LIFT_PRIOR, baseline_rate=BASELINE_RATE),\n", + " {\"lift\": 0.015},\n", + ")\n", + "demo_draw_bern = pm.sample_prior_predictive(1, model=demo_model_bern, random_seed=RANDOM_SEED)\n", + "n_A_demo = int(demo_draw_bern.prior[\"n_A\"].values.reshape(-1)[0])\n", + "n_B_demo = int(demo_draw_bern.prior[\"n_B\"].values.reshape(-1)[0])\n", + "\n", + "with bernoulli_two_arm_model(\n", + " n_A_demo, n_B_demo, N=4000, baseline_rate=BASELINE_RATE, kappa=BETA_PRIOR_KAPPA\n", + "):\n", + " idata_bern_demo = pm.sample(\n", + " draws=1000,\n", + " tune=1000,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )\n", + "\n", + "pc = az.plot_dist(\n", + " idata_bern_demo,\n", + " var_names=[\"lift\"],\n", + " visuals={\"title\": {\"text\": r\"Posterior on conversion lift at $N=4000$\"}},\n", + ")\n", + "az.add_lines(\n", + " pc,\n", + " values=0.0,\n", + " visuals={\"ref_line\": {\"color\": \"C1\", \"label\": \"ref = 0.0\"}},\n", + ")\n", + "pc.get_viz(\"plot\").legend()" + ] + }, + { + "cell_type": "markdown", + "id": "005827fd", + "metadata": {}, + "source": [ + "The PyMC posterior on lift agrees with the conjugate Beta posterior, as it must under this setup. The decision rule is the same, and the ceiling is lower because the planning prior carries a smaller probability that the lift is positive. That prior probability sets the asymptote that no sample size can exceed.\n", + "\n", + "## The cost of an under-informed prior\n", + "\n", + "The assurance curve is conditional on the prior. A tightly informative prior centred near the truth produces an optimistic-looking curve; a flat prior produces a curve that requires substantially more data to reach the same assurance. Neither is wrong. They report what each prior commitment buys the planner." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "279cd463", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:16.117411Z", + "iopub.status.busy": "2026-06-01T17:16:16.117300Z", + "iopub.status.idle": "2026-06-01T17:16:23.592971Z", + "shell.execute_reply": "2026-06-01T17:16:23.592185Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 923, + "width": 3023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "INFORMED_PRIOR = EffectPrior(mu=0.4, sigma=0.3)\n", + "FLAT_PRIOR = EffectPrior(mu=0.4, sigma=1.5)\n", + "SCEPTICAL_PRIOR = EffectPrior(mu=0.1, sigma=0.5)\n", + "\n", + "prior_comparison = {}\n", + "for name, prior in [\n", + " (\"Informed\", INFORMED_PRIOR),\n", + " (\"Flat\", FLAT_PRIOR),\n", + " (\"Sceptical\", SCEPTICAL_PRIOR),\n", + "]:\n", + " df = assurance_curve(\n", + " gaussian_assurance_at_N,\n", + " N_grid=N_GRID,\n", + " n_sims=N_SIMS,\n", + " rng=np.random.default_rng(RANDOM_SEED),\n", + " prior=prior,\n", + " sigma_obs=SIGMA_OBS,\n", + " threshold=DECISION_THRESHOLD,\n", + " )\n", + " prior_comparison[name] = df\n", + "\n", + "fig, ax = plt.subplots(figsize=(15, 4.5))\n", + "for name, df in prior_comparison.items():\n", + " ax.plot(df[\"N\"], df[\"assurance\"], marker=\"o\", linewidth=2, label=name)\n", + "ax.set_xscale(\"log\")\n", + "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n", + "ax.set_xlabel(\"Sample size per arm\")\n", + "ax.set_ylabel(\"Assurance\")\n", + "ax.set_title(\"Assurance under three prior commitments\")\n", + "ax.legend();" + ] + }, + { + "cell_type": "markdown", + "id": "84fb1b32", + "metadata": {}, + "source": [ + "## Design prior and analysis prior\n", + "\n", + "The assurance loop carries two priors with distinct jobs. The *design prior* generates the synthetic worlds the experiment will face. The *analysis prior* reads each dataset and forms the posterior the decision rule consults. Every curve so far set the two equal. Separating them measures a sensitivity the FDA guidance asks for directly: how the operating characteristics respond when the inference commitment disagrees with the planning belief {cite:p}`fda2026bayesian`. The generative model already carries the design prior and the inference model the analysis prior, so the loop runs the mismatch with one extra argument." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "142452a1", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n", + "Sampling: [delta, y_A, y_B]\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 923, + "width": 3023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "OPTIMISTIC_DESIGN = EffectPrior(mu=0.6, sigma=0.4)\n", + "SCEPTICAL_ANALYSIS = EffectPrior(mu=0.0, sigma=0.3)\n", + "\n", + "design_analysis_cases = {\n", + " \"Matched (design = analysis)\": (OPTIMISTIC_DESIGN, OPTIMISTIC_DESIGN),\n", + " \"Optimistic design, sceptical analysis\": (OPTIMISTIC_DESIGN, SCEPTICAL_ANALYSIS),\n", + " \"Sceptical design, optimistic analysis\": (SCEPTICAL_ANALYSIS, OPTIMISTIC_DESIGN),\n", + "}\n", + "\n", + "design_analysis_curves = {}\n", + "for name, (design_prior, analysis_prior) in design_analysis_cases.items():\n", + " design_analysis_curves[name] = assurance_curve(\n", + " gaussian_assurance_at_N,\n", + " N_grid=N_GRID,\n", + " n_sims=N_SIMS,\n", + " rng=np.random.default_rng(RANDOM_SEED),\n", + " prior=design_prior,\n", + " analysis_prior=analysis_prior,\n", + " sigma_obs=SIGMA_OBS,\n", + " threshold=DECISION_THRESHOLD,\n", + " )\n", + "\n", + "fig, ax = plt.subplots(figsize=(15, 4.5))\n", + "for name, df in design_analysis_curves.items():\n", + " ax.plot(df[\"N\"], df[\"assurance\"], marker=\"o\", linewidth=2, label=name)\n", + "ax.set_xscale(\"log\")\n", + "ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n", + "ax.set_xlabel(\"Sample size per arm\")\n", + "ax.set_ylabel(\"Assurance\")\n", + "ax.set_title(\"Assurance when the design and analysis priors agree or disagree\")\n", + "ax.legend();" + ] + }, + { + "cell_type": "markdown", + "id": "e0ff8d8a", + "metadata": {}, + "source": [ + "A sceptical analysis prior lowers assurance at every sample size, because it discounts the same evidence the optimistic design prior expects to see. The reverse pairing recovers most of the matched curve once the data accumulate, since an optimistic analysis prior and a growing dataset agree. The gap between the curves is the price of a mismatch, and it narrows as $N$ grows. Small experiments pay the most for an analysis prior that disagrees with the design belief, which matches the guidance observation that trial characteristics are most sensitive to the analysis prior when the sample size is small {cite:p}`fda2026bayesian`." + ] + }, + { + "cell_type": "markdown", + "id": "eb131822", + "metadata": {}, + "source": [ + "## The information content of a prior: effective sample size\n", + "\n", + "The three curves above differ because the three priors carry different amounts of information. The *prior effective sample size* (ESS) makes this precise: it is the number of actual experimental observations the prior is equivalent to in terms of information content. A prior with ESS of 128 is, before the first participant is enrolled, already as informative as 128 observed subjects per arm.\n", + "\n", + "For the two-arm Gaussian trial the ESS follows from equating information in the prior with information from $n$ observations. The prior $\\mathcal{N}(\\mu_0, \\sigma_0^2)$ carries information $1/\\sigma_0^2$; the effect estimate from $n$ observations carries $n / 2\\sigma_{\\text{obs}}^2$. Setting them equal:\n", + "\n", + "$$n_{\\text{ESS}} = \\frac{2\\sigma_{\\text{obs}}^2}{\\sigma_0^2}$$\n", + "\n", + "The simulation-based approach recovers the same number without the closed form. For each $N$ in a grid, draw synthetic datasets from the prior predictive and compute the posterior variance under a flat reference prior; the $N^*$ where the average posterior variance crosses the prior variance is the ESS. The machinery is the same prior-predictive loop already running in the assurance calculation; only the inner step changes. In the conjugate case the analytical posterior fills that step. In non-conjugate models such as hierarchical likelihoods or logistic regression, the same loop runs with MCMC posteriors and the ESS estimate generalises without modification. Verifying that analytical and simulation estimates agree for the Gaussian case validates the approach for those more complex settings." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "8518b730", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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prior_muprior_sigmaanalytical_ESS
Informed0.40.3355.6
Default0.40.5128.0
Flat0.41.514.2
Sceptical0.10.5128.0
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" + ], + "text/plain": [ + " prior_mu prior_sigma analytical_ESS\n", + "Informed 0.4 0.3 355.6\n", + "Default 0.4 0.5 128.0\n", + "Flat 0.4 1.5 14.2\n", + "Sceptical 0.1 0.5 128.0" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def analytical_ess(prior, sigma_obs):\n", + " \"\"\"Prior ESS for a two-arm Gaussian trial: 2σ²_obs / σ²_prior.\"\"\"\n", + " return 2 * sigma_obs**2 / prior.sigma**2\n", + "\n", + "\n", + "pd.DataFrame(\n", + " {\n", + " \"prior_mu\": [p.mu for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]],\n", + " \"prior_sigma\": [\n", + " p.sigma for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]\n", + " ],\n", + " \"analytical_ESS\": [\n", + " analytical_ess(p, SIGMA_OBS)\n", + " for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]\n", + " ],\n", + " },\n", + " index=[\"Informed\", \"Default\", \"Flat\", \"Sceptical\"],\n", + ").round(1)" + ] + }, + { + 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prior_sigmaanalytical_ESSsimulation_ESS
Informed0.3355.6357.1
Default0.5128.0128.1
Flat1.514.214.3
Sceptical0.5128.0128.1
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" + ], + "text/plain": [ + " prior_sigma analytical_ESS simulation_ESS\n", + "Informed 0.3 355.6 357.1\n", + "Default 0.5 128.0 128.1\n", + "Flat 1.5 14.2 14.3\n", + "Sceptical 0.5 128.0 128.1" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def simulation_based_ess(prior, sigma_obs, N_grid, n_sims, rng):\n", + " \"\"\"\n", + " Estimate prior ESS via simulation: find N* where the mean posterior variance\n", + " under a flat reference prior crosses the prior variance.\n", + "\n", + " Uses the same prior-predictive sampling as the assurance loop. Replace\n", + " gaussian_posterior_delta with an MCMC posterior to extend to non-conjugate models.\n", + " \"\"\"\n", + " flat_ref = EffectPrior(mu=0.0, sigma=10 * sigma_obs)\n", + " target_var = prior.sigma**2\n", + " records = []\n", + " for N in N_grid:\n", + " N = int(N)\n", + " seed = int(rng.integers(2**31 - 1))\n", + " pp = pm.sample_prior_predictive(\n", + " n_sims, model=gaussian_generative_model(N, prior), random_seed=seed\n", + " )\n", + " y_A = pp.prior[\"y_A\"].values.reshape(n_sims, N)\n", + " y_B = pp.prior[\"y_B\"].values.reshape(n_sims, N)\n", + " d_hat = y_B.mean(axis=1) - y_A.mean(axis=1)\n", + " _, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, flat_ref)\n", + " records.append({\"N\": N, \"mean_post_var\": float(np.mean(post_sd**2))})\n", + " df = pd.DataFrame(records)\n", + " post_vars = df[\"mean_post_var\"].values\n", + " N_vals = df[\"N\"].values.astype(float)\n", + " # post_var decreases with N; interpolate to find where it crosses the prior variance\n", + " ess_sim = float(np.interp(target_var, post_vars[::-1], N_vals[::-1]))\n", + " return ess_sim, df\n", + "\n", + "\n", + "N_ESS_GRID = np.unique(np.round(np.geomspace(10, 600, 30)).astype(int))\n", + "N_ESS_SIMS = 200\n", + "ess_rng = np.random.default_rng(RANDOM_SEED + 99)\n", + "\n", + "ess_results = {}\n", + "for name, prior in [\n", + " (\"Informed\", INFORMED_PRIOR),\n", + " (\"Default\", EFFECT_PRIOR),\n", + " (\"Flat\", FLAT_PRIOR),\n", + " (\"Sceptical\", SCEPTICAL_PRIOR),\n", + "]:\n", + " ess_a = analytical_ess(prior, SIGMA_OBS)\n", + " ess_s, df_curve = simulation_based_ess(prior, SIGMA_OBS, N_ESS_GRID, N_ESS_SIMS, ess_rng)\n", + " ess_results[name] = {\n", + " \"prior\": prior,\n", + " \"ess_analytical\": ess_a,\n", + " \"ess_sim\": ess_s,\n", + " \"curve\": df_curve,\n", + " }\n", + "\n", + "pd.DataFrame(\n", + " {\n", + " \"prior_sigma\": {n: v[\"prior\"].sigma for n, v in ess_results.items()},\n", + " \"analytical_ESS\": {n: round(v[\"ess_analytical\"], 1) for n, v in ess_results.items()},\n", + " \"simulation_ESS\": {n: round(v[\"ess_sim\"], 1) for n, v in ess_results.items()},\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "839ea69e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 1023, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(20, 5))\n", + "\n", + "# Left: ESS crossing picture for the default prior\n", + "res = ess_results[\"Default\"]\n", + "curve = res[\"curve\"]\n", + "prior_d = res[\"prior\"]\n", + "ess_a_d = res[\"ess_analytical\"]\n", + "ess_s_d = res[\"ess_sim\"]\n", + "\n", + "axes[0].plot(\n", + " curve[\"N\"],\n", + " curve[\"mean_post_var\"],\n", + " marker=\"o\",\n", + " color=\"C0\",\n", + " markersize=4,\n", + " label=\"Mean posterior variance (flat prior)\",\n", + ")\n", + "axes[0].axhline(\n", + " prior_d.sigma**2,\n", + " color=\"C3\",\n", + " linestyle=\"--\",\n", + " label=rf\"Prior variance $\\sigma_0^2$ = {prior_d.sigma**2:.2f}\",\n", + ")\n", + "axes[0].axvline(\n", + " ess_a_d,\n", + " color=\"C2\",\n", + " linestyle=\":\",\n", + " linewidth=2,\n", + " label=f\"Analytical ESS = {ess_a_d:.0f}\",\n", + ")\n", + "axes[0].axvline(\n", + " ess_s_d,\n", + " color=\"C3\",\n", + " linestyle=\":\",\n", + " linewidth=2,\n", + " alpha=0.7,\n", + " label=f\"Simulation ESS ≈ {ess_s_d:.0f}\",\n", + ")\n", + "axes[0].set_xlabel(\"N per arm\")\n", + "axes[0].set_ylabel(\"Mean posterior variance under flat prior\")\n", + "axes[0].set_title(r\"ESS crossing: default prior ($\\sigma_0 = 0.5$)\")\n", + "axes[0].legend()\n", + "\n", + "# Right: assurance curves with ESS positions annotated\n", + "for name in [\"Informed\", \"Flat\", \"Sceptical\"]:\n", + " res = ess_results[name]\n", + " df = prior_comparison[name]\n", + " ess_a = res[\"ess_analytical\"]\n", + " axes[1].plot(\n", + " df[\"N\"],\n", + " df[\"assurance\"],\n", + " marker=\"o\",\n", + " linewidth=2,\n", + " label=f\"{name} (ESS ≈ {ess_a:.0f})\",\n", + " )\n", + " axes[1].axvline(ess_a, linestyle=\":\", alpha=0.35)\n", + "\n", + "axes[1].set_xscale(\"log\")\n", + "axes[1].xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f\"{int(x):,}\"))\n", + "axes[1].set_xlabel(\"Sample size per arm\")\n", + "axes[1].set_ylabel(\"Assurance\")\n", + "axes[1].set_title(\"Assurance curves with ESS marked\")\n", + "axes[1].legend();" + ] + }, + { + "cell_type": "markdown", + "id": "95945bca", + "metadata": {}, + "source": [ + "The left panel is a calibration check. The simulation curve, posterior variance under a flat prior as a function of N, crosses the prior variance at the point the analytical formula predicts. The two estimates agree to within interpolation noise. For non-conjugate models where no closed form for the posterior variance exists, the same loop with MCMC posteriors in place of `gaussian_posterior_delta` gives the correct ESS. The conjugate case validates the simulation approach before the closed form disappears.\n", + "\n", + "The right panel reads the ESS against the assurance curves. The dotted vertical lines mark each prior's ESS on the sample-size axis. An ESS of 356 (Informed) means the prior carries more information than 350 subjects per arm before the first participant is enrolled; the curve climbs steeply early because the prior is already doing most of the work. An ESS of 14 (Flat) means the prior contributes almost nothing, and every observation earns its full weight. The ESS converts the abstract question \"how informative is this prior?\" into a number on the same axis as the assurance curve: experiments whose planned N falls well below the ESS are prior-dominated; those well above it are data-dominated.\n", + "\n", + "This is the quantitative form of the trade-off the sensitivity analysis in {ref}`sensitivity_confounding` interrogates from the other side. There, the question is what happens when that committed information meets an identification gap, and the tipping point at which the conclusion turns measures how much that committed ESS has put at risk." + ] + }, + { + "cell_type": "markdown", + "id": "fda04dc5", + "metadata": {}, + "source": [ + "The three curves disagree most where they should: at small sample sizes where the data has not yet overwhelmed the prior. The informed prior reaches high assurance fastest because it is willing to commit to a narrow effect range; the sceptical prior assumes a smaller effect and so needs more data to detect it; the flat prior carries enough probability mass over zero that even moderate datasets do not push the posterior reliably above the decision threshold. The point is to make the dependence of the assurance number on the prior commitment visible, so the prior becomes a subject of negotiation rather than a hidden choice.\n", + "\n", + "## Planning as a posterior over future posteriors\n", + "\n", + "The experiment we have not yet run is a posterior we have not yet computed. What we have is a prior, a model, and the patience to ask what the experiment will likely say.\n", + "\n", + "Statistical power questions answers a conditional: given a specific effect, what probability of detection? Bayesian assurance answers a marginal question: given everything currently believed, what probability that the inference about to be drawn will be useful? The operation that produces assurance is the same one that will produce the posterior at the end of the experiment - only the data are still hypothetical. Assurance makes explicit the assumption power leaves buried, a believed distribution of effects, and derives from that assumption a posterior to evaluate.\n", + "\n", + "The Gaussian case and the Bernoulli case ran the same inference machinery. What changed was the likelihood, and with it the ceiling its geometry sets on how much assurance any sample size can buy. The next notebook, {ref}`sensitivity_confounding`, keeps the machinery and changes the question: not what an experiment will probably say, but what it did say once clean identification is itself in doubt.\n", + "\n", + "## Authors\n", + "\n", + "- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026.\n", + "\n", + "## References\n", + "\n", + ":::{bibliography}\n", + ":filter: docname in docnames\n", + ":::\n", + "\n", + "## Watermark" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "b30e957b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:16:23.594569Z", + "iopub.status.busy": "2026-06-01T17:16:23.594445Z", + "iopub.status.idle": "2026-06-01T17:16:23.605251Z", + "shell.execute_reply": "2026-06-01T17:16:23.604855Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last updated: Mon, 29 Jun 2026\n", + "\n", + "Python implementation: CPython\n", + "Python version : 3.13.13\n", + "IPython version : 9.14.0\n", + "\n", + "pytensor: 3.0.3\n", + "xarray : 2026.4.0\n", + "\n", + "arviz : 1.1.0\n", + "matplotlib: 3.10.9\n", + "numpy : 2.3.5\n", + "pandas : 2.3.3\n", + "pymc : 6.0.1\n", + "scipy : 1.17.1\n", + "\n", + "Watermark: 2.6.0\n", + "\n" + ] + } + ], + "source": [ + "%load_ext watermark\n", + "%watermark -n -u -v -iv -w -p pytensor,xarray" + ] + }, + { + "cell_type": "markdown", + "id": "dbbeeb58", + "metadata": {}, + "source": [ + ":::{include} ../page_footer.md\n", + ":::" + ] + } + ], + "metadata": { + "jupytext": { + "default_lexer": "ipython3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/causal_inference/assurance_planning_simulation.myst.md b/examples/causal_inference/assurance_planning_simulation.myst.md new file mode 100644 index 000000000..00c624d6d --- /dev/null +++ b/examples/causal_inference/assurance_planning_simulation.myst.md @@ -0,0 +1,785 @@ +--- +jupytext: + default_lexer: ipython3 + text_representation: + extension: .md + format_name: myst + format_version: 0.13 +kernelspec: + display_name: Python 3 + language: python + name: python3 +--- + +(assurance_planning)= +# Assurance Planning via Simulation + +:::{post} May 2026 +:tags: experimentation, decision analysis, power analysis, assurance, simulation +:category: intermediate, reference +:author: Nathaniel Forde +::: + +:::{figure} experimentation_triptych.jpeg +:name: experimentation-triptych +:width: 100% +:align: center + +The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance (this notebook):* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis:* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis:* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery. +::: + +Experimental questions are seeded in the science that preceded them. Answers are stress-tested and refined. New experiments spawn further questions again. This is the cycle. + +## The question planners are actually asking + +When we experiment, we encode questions. Implicitly we assume an answer will be useful. Our hypotheses are "operationalised" as power heuristics: given an effect size, what is the probability we cross a fixed threshold? This is an indirect and contorted gauge of efficacy. Instead of asking whether the treatment is effective, we often ask whether the results are surprising assuming a degree of effectiveness. The slippage between these two questions has produced a generation of experimental plans calibrated to invented effect sizes rather than to the beliefs the planners actually hold. + +An alternative is Bayesian Assurance. The construction is mechanical: draw from the priors, generate a dataset, fit the treatment model, apply the decision rule, repeat. The result is a single number: the probability the experiment will conclude what its stakeholders need. The process is the same whether the response is continuous (like revenue per visitor) or binary (like conversion); we develop it on the Gaussian case first and confirm the process is invariant to the response scale. This notebook is the first of three on the lifecycle of a Bayesian experiment; see {ref}`sensitivity_confounding` for the interpretation counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The same inferential machinery serves all three panels of the triptych, but what changes is the problem put to it. + +:::{admonition} Where this lands in regulatory practice +:class: note + +We are going to apply Bayesian assurance to a question in product-analytics but the technique has a wider application. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials defines *Bayesian power* as the probability of meeting the success criterion averaged over a prior distribution {cite:p}`fda2026bayesian`, which is assurance under another name. The FDA guidance formalises the success rule as $\Pr(\text{effect} > a) > c$ (the rule used below, with $a = 0$ and $c = 0.95$). The same guidance separates the *design prior* that generates the synthetic trials from the *analysis prior* used in inference. The generative and inference models below are distinct objects for this reason. Below we'll runs the assurance loop with the two priors deliberately mismatched. The clinical trial setting in the FDA report differs from product experimentation; the machinery is identical. +::: + +```{code-cell} ipython3 +import warnings + +from dataclasses import dataclass + +import arviz as az +import matplotlib.pyplot as plt +import matplotlib.ticker as mticker +import numpy as np +import pandas as pd +import pymc as pm + +from scipy import stats + +warnings.filterwarnings("ignore", category=RuntimeWarning) +warnings.filterwarnings("ignore", category=UserWarning) +``` + +```{code-cell} ipython3 +%config InlineBackend.figure_format = 'retina' +az.style.use("arviz-variat") +rng = np.random.default_rng(42) +RANDOM_SEED = 42 +``` + +### The scenario + +An e-commerce team is evaluating a redesigned checkout flow. We cover two outcomes: the continuous outcome is revenue per visitor, the binary outcome is conversion. We will not commit to a particular vertical or product; the structure is generic to any A/B test with one of these outcome types. What matters is that the same prior beliefs and the same decision rule will be asked of two different likelihoods. The Gaussian case will carry the argument; the Bernoulli case will confirm it travels. + +```{code-cell} ipython3 +@dataclass +class EffectPrior: + """Prior beliefs about a treatment effect, on the scale of the outcome.""" + + mu: float + sigma: float + + def sample(self, rng, size=1): + return rng.normal(self.mu, self.sigma, size=size) +``` + +## Power and assurance: two questions, different focus + +Power and assurance share an interface and answer different questions. Power conditions on a specific effect size $\theta_0$ that the planner has been pressed into naming, and computes the probability of rejecting the null at that value: + +$$ +\text{Power}(N) = P\!\left(\text{reject } H_0 \mid \theta = \theta_0,\; N\right). +$$ + +The conditioning bar is the load-bearing part. The planner who has confidently named $\theta_0$ has implicitly used up the uncertainty that motivated the experiment in the first place. Assurance refuses the substitution. Instead it integrates over the planner's prior beliefs about the effect. The decision rule is whether the posterior probability of a positive effect clears a threshold $c$: + +$$ +\text{Assurance}(N) = \mathbb{E}_{\substack{\theta \,\sim\, \pi(\theta) \\ \hat{d} \,\sim\, p(\hat{d} \mid \theta,\, N)}}\!\left[\mathbb{1}\!\bigl(P(\theta > 0 \mid \hat{d},\, N) > c\bigr)\right]. +$$ + +The outer expectation averages over effect sizes drawn from the prior; the inner averages over data generated under each effect ({cite:p}`ohagan2005assurance`, {cite:p}`spiegelhalter2004bayesian`). The integration is the entire move. Where power asks the planner to invent a world, assurance asks them to describe the one they already believe they are in. With that description in place, we can quantify how likely the result is when conditioned on the prior distribution. + +## The simulation engine + +Assurance is an expectation over the *prior predictive distribution*: the joint distribution of effect and data that the model generates before any real data arrive. As a Monte Carlo estimator the integral becomes a procedure in three steps, repeated for each candidate sample size: + +1. **Sample the prior predictive** of an unconditioned generative model. Each draw is a complete synthetic experiment: an effect drawn from the prior, and a dataset of size $N$ generated under it. +2. **Fit the analysis model** to each synthetic dataset and apply the decision rule. +3. **Record** the fraction of synthetic experiments in which the decision succeeded. + +Drawing a truth and generating data under it is exactly what `pm.sample_prior_predictive` does on a model with no observed data, so we let PyMC's generative machinery produce the synthetic experiments rather than hand-rolling the sampling with `numpy`. The generative model that produces the data and the inference model that analyses it are separate objects, and keeping them separate is the point: the generative model encodes the worlds we are planning for, the inference model encodes how we will reason once real data arrive. This workflow is defined as a function and passed through a sample size grid to determine how many _N_ is required to achieve surety in the finding. + +```{code-cell} ipython3 +def assurance_curve(assurance_fn, N_grid, n_sims, rng, **kwargs): + """Estimate the assurance curve by evaluating assurance at each sample size.""" + records = [] + for N in N_grid: + a = assurance_fn(N=int(N), n_sims=n_sims, rng=rng, **kwargs) + records.append({"N": int(N), "assurance": a}) + return pd.DataFrame(records) +``` + +## Gaussian outcome: revenue per visitor + +The Gaussian case is the cleanest place to make the mechanics explicit. Each arm produces a revenue-per-visitor outcome with known noise scale $\sigma_{\text{obs}}$ (we treat this as known here; in practice it is estimated from a pilot or historical data). The team is interested in the treatment effect $\delta = \mu_B - \mu_A$, and holds a prior over $\delta$ informed by past experiments in similar product surfaces. That prior is not conjured from nothing: {ref}`meta_analysis_experiments` shows how a meta-analysis of past experiments produces exactly this kind of prior, so the synthesis at the end of one experiment's lifecycle is the planning input at the start of the next. Concretely, the meta-analytic predictive there closes on $\mathcal{N}(0.4, 0.5)$, which is exactly the `EFFECT_PRIOR` defined below: the number that ends that notebook opens this one. + +Two models do the work. The *generative model* is unconditioned: it places the planning prior on $\delta$ and generates synthetic datasets, and it is the object we hand to `pm.sample_prior_predictive`. The *inference model* conditions on a dataset and returns the posterior on $\delta$; the decision rule asks whether the posterior probability of a positive effect exceeds a threshold (0.95 below). For the assurance loop the conjugate Normal–Normal posterior on $\delta$ admits a closed form, which lets us evaluate the decision on each synthetic experiment without running MCMC every time. + +We will verify that closed form against the inference model's MCMC posterior at a single sample size before relying on it. This also underwrites the idea that we can use MCMC for this procedure even with more complex models. + +```{code-cell} ipython3 +SIGMA_OBS = 4.0 +DECISION_THRESHOLD = 0.95 +BASELINE_REVENUE = 10.0 +# Not free-floating: this is the meta-analytic predictive for a new market from +# the synthesis notebook (meta_analysis_experiments), which closes on N(0.4, 0.5). +EFFECT_PRIOR = EffectPrior(mu=0.4, sigma=0.5) + + +def gaussian_generative_model(N, prior): + """Unconditioned model: planning prior on the effect plus the data-generating likelihood.""" + with pm.Model() as model: + delta = pm.Normal("delta", mu=prior.mu, sigma=prior.sigma) + pm.Normal("y_A", mu=BASELINE_REVENUE, sigma=SIGMA_OBS, shape=N) + pm.Normal("y_B", mu=BASELINE_REVENUE + delta, sigma=SIGMA_OBS, shape=N) + return model + + +def gaussian_two_arm_model(y_A, y_B, prior): + """Inference model: conditions on an observed dataset and returns the posterior on the effect.""" + with pm.Model() as model: + mu_A = pm.Normal("mu_A", mu=BASELINE_REVENUE, sigma=5.0) + delta = pm.Normal("delta", mu=prior.mu, sigma=prior.sigma) + mu_B = pm.Deterministic("mu_B", mu_A + delta) + pm.Normal("obs_A", mu=mu_A, sigma=SIGMA_OBS, observed=y_A) + pm.Normal("obs_B", mu=mu_B, sigma=SIGMA_OBS, observed=y_B) + return model +``` + +A single synthetic experiment makes the inference model concrete. We use the do-operator to fix the generative effect at a chosen value, draw one dataset from the prior predictive, and condition the inference model on it. + +```{code-cell} ipython3 +demo_true_delta = 0.6 +demo_model = pm.do(gaussian_generative_model(N=200, prior=EFFECT_PRIOR), {"delta": demo_true_delta}) +demo_draw = pm.sample_prior_predictive(1, model=demo_model, random_seed=RANDOM_SEED) +y_A_demo = demo_draw.prior["y_A"].values.reshape(-1) +y_B_demo = demo_draw.prior["y_B"].values.reshape(-1) + +with gaussian_two_arm_model(y_A_demo, y_B_demo, EFFECT_PRIOR): + idata_gauss_demo = pm.sample( + draws=1000, + tune=1000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) +``` + +```{code-cell} ipython3 +pc = az.plot_dist( + idata_gauss_demo, + var_names=["delta"], + visuals={"title": {"text": r"Posterior on $\delta$ at $N=200$ (one simulated dataset)"}}, +) +az.add_lines( + pc, + values=0.0, + visuals={"ref_line": {"color": "C1", "label": "ref = 0.0"}}, +) +pc.get_viz("plot").legend(); +``` + +The posterior concentrates above zero; under the decision rule the team would conclude the new flow lifts revenue. That is a single draw of the experiment. Assurance asks how often this conclusion would arrive if we re-ran the experiment many times under our actual prior. + +The conjugate posterior on $\delta$ given $\hat d = \bar y_B - \bar y_A$ has mean and variance: + +$$ +\sigma_d^2 = \frac{2\sigma_{\text{obs}}^2}{N}, \quad +\tau^2_{\text{post}} = \left(\frac{1}{\tau_0^2} + \frac{1}{\sigma_d^2}\right)^{-1}, \quad +\mu_{\text{post}} = \tau^2_{\text{post}}\left(\frac{\mu_0}{\tau_0^2} + \frac{\hat d}{\sigma_d^2}\right), +$$ + +where $(\mu_0, \tau_0)$ is the prior on $\delta$. We check this matches the PyMC posterior before relying on it. + +```{code-cell} ipython3 +def gaussian_posterior_delta(d_hat, N, sigma_obs, prior): + sigma_d_sq = 2 * sigma_obs**2 / N + post_var = 1.0 / (1.0 / prior.sigma**2 + 1.0 / sigma_d_sq) + post_mean = post_var * (prior.mu / prior.sigma**2 + d_hat / sigma_d_sq) + return post_mean, np.sqrt(post_var) + + +d_hat_demo = y_B_demo.mean() - y_A_demo.mean() +analytical_mu, analytical_sd = gaussian_posterior_delta( + d_hat_demo, N=200, sigma_obs=SIGMA_OBS, prior=EFFECT_PRIOR +) +mcmc_mu = idata_gauss_demo.posterior["delta"].mean().item() +mcmc_sd = idata_gauss_demo.posterior["delta"].std().item() + +pd.DataFrame( + {"analytical": [analytical_mu, analytical_sd], "MCMC": [mcmc_mu, mcmc_sd]}, + index=["posterior mean of delta", "posterior sd of delta"], +).round(3) +``` + +The two posteriors agree to within MCMC noise. Now we get to the heart of the technique and push our procedure through different sample values of _N_. + +```{code-cell} ipython3 +def gaussian_assurance_at_N(N, n_sims, prior, sigma_obs, threshold, rng, analysis_prior=None): + # `prior` is the design prior: it generates the synthetic worlds. `analysis_prior` + # is used to form the posterior; it defaults to the design prior so a single + # argument reproduces the matched-prior case. + analysis_prior = prior if analysis_prior is None else analysis_prior + seed = int(rng.integers(2**31 - 1)) + pp = pm.sample_prior_predictive( + n_sims, model=gaussian_generative_model(N, prior), random_seed=seed + ) + y_A = pp.prior["y_A"].values.reshape(n_sims, N) + y_B = pp.prior["y_B"].values.reshape(n_sims, N) + d_hat = y_B.mean(axis=1) - y_A.mean(axis=1) + post_mu, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, analysis_prior) + prob_positive = 1.0 - stats.norm.cdf(0.0, loc=post_mu, scale=post_sd) + return float((prob_positive > threshold).mean()) + + +N_GRID = np.array([100, 200, 400, 800, 1600, 3200, 6400]) +N_SIMS = 1000 + +assurance_df = assurance_curve( + gaussian_assurance_at_N, + N_grid=N_GRID, + n_sims=N_SIMS, + rng=np.random.default_rng(RANDOM_SEED), + prior=EFFECT_PRIOR, + sigma_obs=SIGMA_OBS, + threshold=DECISION_THRESHOLD, +) +assurance_df +``` + +For each simulated future dataset, we compute the posterior distribution of the treatment effect and evaluate the posterior probability that the effect is positive, `prob_positive`. A trial is considered decisive if `prob_positive` exceeds the pre-specified `DECISION_THRESHOLD`. The Bayesian assurance is the proportion of simulated trials that satisfy this decision criterion. As the planned sample size increases, posterior uncertainty decreases, leading to a larger proportion of decisive trials and therefore higher assurance. + +For comparison we compute frequentist power at a single fixed effect size. The convention is to set the effect to the prior mean, which is itself an arbitrary choice, and a revealing one. + +```{code-cell} ipython3 +def gaussian_power(N, delta_alt, sigma_obs, alpha=0.05): + sigma_d = np.sqrt(2 * sigma_obs**2 / N) + z_crit = stats.norm.ppf(1 - alpha) + return 1.0 - stats.norm.cdf(z_crit - delta_alt / sigma_d) + + +power_at_prior_mean = np.array([gaussian_power(N, EFFECT_PRIOR.mu, SIGMA_OBS) for N in N_GRID]) +power_at_optimistic = np.array( + [gaussian_power(N, EFFECT_PRIOR.mu + EFFECT_PRIOR.sigma, SIGMA_OBS) for N in N_GRID] +) +power_at_pessimistic = np.array( + [gaussian_power(N, max(EFFECT_PRIOR.mu - EFFECT_PRIOR.sigma, 0.01), SIGMA_OBS) for N in N_GRID] +) + +prior_prob_positive = 1.0 - stats.norm.cdf(0.0, EFFECT_PRIOR.mu, EFFECT_PRIOR.sigma) + +fig, ax = plt.subplots(figsize=(15, 5.5)) +ax.plot(N_GRID, assurance_df["assurance"], marker="o", linewidth=2, label="Assurance (Bayesian)") +ax.plot( + N_GRID, + power_at_prior_mean, + marker="s", + linestyle="--", + label=r"Power at $\theta_0 = \mu_{\text{prior}}$", +) +ax.plot( + N_GRID, + power_at_optimistic, + marker="^", + linestyle=":", + alpha=0.7, + label=r"Power at $\mu + \sigma$", +) +ax.plot( + N_GRID, + power_at_pessimistic, + marker="v", + linestyle=":", + alpha=0.7, + label=r"Power at $\mu - \sigma$", +) +ax.axhline( + prior_prob_positive, + color="C0", + linestyle="-.", + alpha=0.6, + label=rf"Assurance ceiling $P(\delta>0)$ = {prior_prob_positive:.2f}", +) +ax.set_xscale("log") +ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f"{int(x):,}")) +ax.set_xlabel("Sample size per arm") +ax.set_ylabel("Probability of declaring uplift") +ax.set_title("Assurance vs frequentist power, Gaussian outcome") +ax.legend(loc="lower right", fontsize=9); +``` + +The three power curves fan out because each conditions on a single assumed world. Power at $\mu + \sigma$ assumes an effect of $0.9$ and saturates almost immediately; power at $\mu - \sigma$ is pinned near the test's five-percent floor, because $\mu - \sigma$ lands at essentially zero effect, where even large samples gain almost no detection. Power at the prior mean is the curve a frequentist planner would actually quote. The assurance curve is the prior-weighted integral across the entire fan, and it tells a different story than any single power calculation. + +The story is in the crossing. Between $N=400$ and $N=800$ the assurance curve drops below power-at-the-mean, having sat above it at smaller samples. At small samples assurance is buoyed by the optimistic tail of the prior: it counts the plausible draws above $0.4$, effects of $0.8$ or $1.0$ that even a hundred observations have a real chance of detecting, which the single-point power calculation never sees. Quoting power at the mean understates what small experiments can do, because it ignores the optimistic tail of the prior that assurance counts. + +At large samples the relationship inverts, and the reason is the ceiling drawn above. Power at a fixed positive effect climbs to one: with enough data an effect of $0.4$ is certain to be detected. Assurance cannot reach one: the prior assigns positive probability to a zero or negative effect. Its asymptote is exactly the prior probability that the effect is beneficial, $P(\delta > 0) \approx 0.79$. No sample size buys more assurance than $P(\delta > 0)$. A planner should know that ceiling before committing to more data, and no point on a power curve reveals it. + +:::{admonition} The minimum detectable effect leads a double life +:class: note + +Power is usually quoted at a "minimum detectable effect" (MDE), and that single number carries more weight than it appears to. Read one way, the MDE is a *utility threshold*: an effect smaller than this is not worth shipping, so failing to detect it does not matter, and powering at the MDE is a coherent design target. Read another way, it is a *forecast*: a quiet assumption that the true effect is about this large and positive, sometimes reverse-engineered from the sample size a team can already afford. The frequentist machinery itself is innocent here, because the false-positive rate $\alpha$ already governs the null case; it is the floor that the $\mu - \sigma$ curve traces. What conditions the null away is the reported summary, "$X\%$ power to detect the MDE", which is computed entirely inside the world where the effect is real and exactly the MDE. Assurance does not abolish this assumption. It relocates it from an implicit point to an explicit prior, where the probability that the effect is null or harmful becomes visible and open to argument. +::: + +## The same machinery on a binary outcome + +The generative model fixes the baseline conversion rate, places the planning prior on the lift, and emits binomial counts per arm. The inference step places Beta priors on the per-arm rates and reads off the posterior probability that the lift is positive ({cite:p}`stucchio2015bayesian`, {cite:p}`kruschke2014doing`). + +```{code-cell} ipython3 +BASELINE_RATE = 0.10 +RATE_LIFT_PRIOR = EffectPrior(mu=0.005, sigma=0.012) +BETA_PRIOR_KAPPA = 200 # prior concentration, in units of pseudo-observations +prior_prob_lift_positive = 1.0 - stats.norm.cdf(0.0, RATE_LIFT_PRIOR.mu, RATE_LIFT_PRIOR.sigma) + + +def beta_prior_params(p_mean, kappa): + return kappa * p_mean, kappa * (1 - p_mean) + + +def bernoulli_generative_model(N, rate_prior, baseline_rate): + """Unconditioned model: fixed baseline rate, planning prior on the lift, binomial counts per arm.""" + with pm.Model() as model: + lift = pm.Normal("lift", mu=rate_prior.mu, sigma=rate_prior.sigma) + p_B = pm.Deterministic("p_B", pm.math.clip(baseline_rate + lift, 1e-4, 1 - 1e-4)) + pm.Binomial("n_A", n=N, p=baseline_rate) + pm.Binomial("n_B", n=N, p=p_B) + return model + + +def bernoulli_assurance_at_N( + N, n_sims, rate_prior, baseline_rate, kappa, threshold, rng, n_post=2000 +): + seed = int(rng.integers(2**31 - 1)) + pp = pm.sample_prior_predictive( + n_sims, + model=bernoulli_generative_model(N, rate_prior, baseline_rate), + random_seed=seed, + ) + n_A = pp.prior["n_A"].values.reshape(-1).astype(int) + n_B = pp.prior["n_B"].values.reshape(-1).astype(int) + actual_sims = len(n_A) # PyMC v6 may return fewer draws than requested + alpha0, beta0 = beta_prior_params(baseline_rate, kappa) + p_A_post = rng.beta(alpha0 + n_A[:, None], beta0 + N - n_A[:, None], size=(actual_sims, n_post)) + p_B_post = rng.beta(alpha0 + n_B[:, None], beta0 + N - n_B[:, None], size=(actual_sims, n_post)) + prob_positive = (p_B_post > p_A_post).mean(axis=1) + return float((prob_positive > threshold).mean()) +``` + +```{code-cell} ipython3 +N_GRID_BERN = np.array([500, 1000, 2000, 4000, 8000, 16000, 32000]) + +assurance_bern_df = assurance_curve( + bernoulli_assurance_at_N, + N_grid=N_GRID_BERN, + n_sims=N_SIMS, + rng=np.random.default_rng(RANDOM_SEED), + rate_prior=RATE_LIFT_PRIOR, + baseline_rate=BASELINE_RATE, + kappa=BETA_PRIOR_KAPPA, + threshold=DECISION_THRESHOLD, +) + + +def bernoulli_power(N, p_A, lift_alt, alpha=0.05): + p_B = p_A + lift_alt + p_bar = 0.5 * (p_A + p_B) + se_null = np.sqrt(2 * p_bar * (1 - p_bar) / N) + se_alt = np.sqrt(p_A * (1 - p_A) / N + p_B * (1 - p_B) / N) + z_crit = stats.norm.ppf(1 - alpha) + return 1.0 - stats.norm.cdf((z_crit * se_null - lift_alt) / se_alt) + + +power_bern_at_prior_mean = np.array( + [bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu) for N in N_GRID_BERN] +) +power_bern_at_optimistic = np.array( + [ + bernoulli_power(N, BASELINE_RATE, RATE_LIFT_PRIOR.mu + RATE_LIFT_PRIOR.sigma) + for N in N_GRID_BERN + ] +) +power_bern_at_pessimistic = np.array( + [ + bernoulli_power(N, BASELINE_RATE, max(RATE_LIFT_PRIOR.mu - RATE_LIFT_PRIOR.sigma, 1e-4)) + for N in N_GRID_BERN + ] +) + +fig, ax = plt.subplots(figsize=(15, 4.5)) +ax.plot( + N_GRID_BERN, + assurance_bern_df["assurance"], + marker="o", + linewidth=2, + label="Assurance (Bayesian)", +) +ax.plot( + N_GRID_BERN, + power_bern_at_prior_mean, + marker="s", + linestyle="--", + label=r"Power at lift $=\mu_{\text{prior}}$", +) +ax.plot( + N_GRID_BERN, + power_bern_at_optimistic, + marker="^", + linestyle=":", + alpha=0.7, + label=r"Power at $\mu + \sigma$", +) +ax.plot( + N_GRID_BERN, + power_bern_at_pessimistic, + marker="v", + linestyle=":", + alpha=0.7, + label=r"Power at $\mu - \sigma$", +) +ax.axhline( + prior_prob_lift_positive, + color="C0", + linestyle="-.", + alpha=0.6, + label=rf"Assurance ceiling $P(\text{{lift}}>0)$ = {prior_prob_lift_positive:.2f}", +) + +ax.set_xscale("log") +ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f"{int(x):,}")) +ax.set_xlabel("Sample size per arm") +ax.set_ylabel("Probability of declaring uplift") +ax.set_title("Assurance vs frequentist power, Bernoulli outcome") +ax.legend(loc="lower right"); +``` + +The conversion-rate version runs the same loop, and the loop discloses something the Gaussian case conceals. The lift is bounded above: how large a positive effect can even be depends on how much room sits above the baseline conversion rate, a constraint the Normal likelihood never faces. The Beta prior on the per-arm rates is parameterised here by a concentration $\kappa$, the number of pseudo-observations at the baseline rate that the prior is equivalent to. Setting $\kappa = 200$ is saying: I am as confident about the baseline as if I had watched 200 trials at that rate. This is a different handle on prior calibration than the Normal's mean and standard deviation pair, and it makes the ceiling claim more precise: the assurance curve asymptotes toward the prior probability that the lift is positive, and what that probability is depends not only on the prior's location and scale but on the scale on which the lift is defined. At a 10\% baseline with a planning prior mean of 0.5\%, the prior splits its mass roughly two to one in favour of a positive lift, and the assurance curve asymptotes there, near 0.66. The same machinery produces a lower ceiling than the Gaussian case because the planning prior commits to a more cautious belief about how large a conversion lift can plausibly be. The generative model produced the synthetic experiments; the conjugate Beta posterior supplied the decision, with no MCMC in the loop. We confirm below that this matches a full PyMC fit on a single dataset, so nothing in the assurance machinery depends on the closed form being available; it depends only on a posterior we can compute reliably. + +```{code-cell} ipython3 +def bernoulli_two_arm_model(n_A, n_B, N, baseline_rate, kappa): + alpha0, beta0 = beta_prior_params(baseline_rate, kappa) + with pm.Model() as model: + p_A = pm.Beta("p_A", alpha=alpha0, beta=beta0) + p_B = pm.Beta("p_B", alpha=alpha0, beta=beta0) + pm.Deterministic("lift", p_B - p_A) + pm.Binomial("obs_A", n=N, p=p_A, observed=n_A) + pm.Binomial("obs_B", n=N, p=p_B, observed=n_B) + return model + + +demo_model_bern = pm.do( + bernoulli_generative_model(N=4000, rate_prior=RATE_LIFT_PRIOR, baseline_rate=BASELINE_RATE), + {"lift": 0.015}, +) +demo_draw_bern = pm.sample_prior_predictive(1, model=demo_model_bern, random_seed=RANDOM_SEED) +n_A_demo = int(demo_draw_bern.prior["n_A"].values.reshape(-1)[0]) +n_B_demo = int(demo_draw_bern.prior["n_B"].values.reshape(-1)[0]) + +with bernoulli_two_arm_model( + n_A_demo, n_B_demo, N=4000, baseline_rate=BASELINE_RATE, kappa=BETA_PRIOR_KAPPA +): + idata_bern_demo = pm.sample( + draws=1000, + tune=1000, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) + +pc = az.plot_dist( + idata_bern_demo, + var_names=["lift"], + visuals={"title": {"text": r"Posterior on conversion lift at $N=4000$"}}, +) +az.add_lines( + pc, + values=0.0, + visuals={"ref_line": {"color": "C1", "label": "ref = 0.0"}}, +) +pc.get_viz("plot").legend() +``` + +The PyMC posterior on lift agrees with the conjugate Beta posterior, as it must under this setup. The decision rule is the same, and the ceiling is lower because the planning prior carries a smaller probability that the lift is positive. That prior probability sets the asymptote that no sample size can exceed. + +## The cost of an under-informed prior + +The assurance curve is conditional on the prior. A tightly informative prior centred near the truth produces an optimistic-looking curve; a flat prior produces a curve that requires substantially more data to reach the same assurance. Neither is wrong. They report what each prior commitment buys the planner. + +```{code-cell} ipython3 +INFORMED_PRIOR = EffectPrior(mu=0.4, sigma=0.3) +FLAT_PRIOR = EffectPrior(mu=0.4, sigma=1.5) +SCEPTICAL_PRIOR = EffectPrior(mu=0.1, sigma=0.5) + +prior_comparison = {} +for name, prior in [ + ("Informed", INFORMED_PRIOR), + ("Flat", FLAT_PRIOR), + ("Sceptical", SCEPTICAL_PRIOR), +]: + df = assurance_curve( + gaussian_assurance_at_N, + N_grid=N_GRID, + n_sims=N_SIMS, + rng=np.random.default_rng(RANDOM_SEED), + prior=prior, + sigma_obs=SIGMA_OBS, + threshold=DECISION_THRESHOLD, + ) + prior_comparison[name] = df + +fig, ax = plt.subplots(figsize=(15, 4.5)) +for name, df in prior_comparison.items(): + ax.plot(df["N"], df["assurance"], marker="o", linewidth=2, label=name) +ax.set_xscale("log") +ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f"{int(x):,}")) +ax.set_xlabel("Sample size per arm") +ax.set_ylabel("Assurance") +ax.set_title("Assurance under three prior commitments") +ax.legend(); +``` + +## Design prior and analysis prior + +The assurance loop carries two priors with distinct jobs. The *design prior* generates the synthetic worlds the experiment will face. The *analysis prior* reads each dataset and forms the posterior the decision rule consults. Every curve so far set the two equal. Separating them measures a sensitivity the FDA guidance asks for directly: how the operating characteristics respond when the inference commitment disagrees with the planning belief {cite:p}`fda2026bayesian`. The generative model already carries the design prior and the inference model the analysis prior, so the loop runs the mismatch with one extra argument. + +```{code-cell} ipython3 +OPTIMISTIC_DESIGN = EffectPrior(mu=0.6, sigma=0.4) +SCEPTICAL_ANALYSIS = EffectPrior(mu=0.0, sigma=0.3) + +design_analysis_cases = { + "Matched (design = analysis)": (OPTIMISTIC_DESIGN, OPTIMISTIC_DESIGN), + "Optimistic design, sceptical analysis": (OPTIMISTIC_DESIGN, SCEPTICAL_ANALYSIS), + "Sceptical design, optimistic analysis": (SCEPTICAL_ANALYSIS, OPTIMISTIC_DESIGN), +} + +design_analysis_curves = {} +for name, (design_prior, analysis_prior) in design_analysis_cases.items(): + design_analysis_curves[name] = assurance_curve( + gaussian_assurance_at_N, + N_grid=N_GRID, + n_sims=N_SIMS, + rng=np.random.default_rng(RANDOM_SEED), + prior=design_prior, + analysis_prior=analysis_prior, + sigma_obs=SIGMA_OBS, + threshold=DECISION_THRESHOLD, + ) + +fig, ax = plt.subplots(figsize=(15, 4.5)) +for name, df in design_analysis_curves.items(): + ax.plot(df["N"], df["assurance"], marker="o", linewidth=2, label=name) +ax.set_xscale("log") +ax.xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f"{int(x):,}")) +ax.set_xlabel("Sample size per arm") +ax.set_ylabel("Assurance") +ax.set_title("Assurance when the design and analysis priors agree or disagree") +ax.legend(); +``` + +A sceptical analysis prior lowers assurance at every sample size, because it discounts the same evidence the optimistic design prior expects to see. The reverse pairing recovers most of the matched curve once the data accumulate, since an optimistic analysis prior and a growing dataset agree. The gap between the curves is the price of a mismatch, and it narrows as $N$ grows. Small experiments pay the most for an analysis prior that disagrees with the design belief, which matches the guidance observation that trial characteristics are most sensitive to the analysis prior when the sample size is small {cite:p}`fda2026bayesian`. + ++++ + +## The information content of a prior: effective sample size + +The three curves above differ because the three priors carry different amounts of information. The *prior effective sample size* (ESS) makes this precise: it is the number of actual experimental observations the prior is equivalent to in terms of information content. A prior with ESS of 128 is, before the first participant is enrolled, already as informative as 128 observed subjects per arm. + +For the two-arm Gaussian trial the ESS follows from equating information in the prior with information from $n$ observations. The prior $\mathcal{N}(\mu_0, \sigma_0^2)$ carries information $1/\sigma_0^2$; the effect estimate from $n$ observations carries $n / 2\sigma_{\text{obs}}^2$. Setting them equal: + +$$n_{\text{ESS}} = \frac{2\sigma_{\text{obs}}^2}{\sigma_0^2}$$ + +The simulation-based approach recovers the same number without the closed form. For each $N$ in a grid, draw synthetic datasets from the prior predictive and compute the posterior variance under a flat reference prior; the $N^*$ where the average posterior variance crosses the prior variance is the ESS. The machinery is the same prior-predictive loop already running in the assurance calculation; only the inner step changes. In the conjugate case the analytical posterior fills that step. In non-conjugate models such as hierarchical likelihoods or logistic regression, the same loop runs with MCMC posteriors and the ESS estimate generalises without modification. Verifying that analytical and simulation estimates agree for the Gaussian case validates the approach for those more complex settings. + +```{code-cell} ipython3 +def analytical_ess(prior, sigma_obs): + """Prior ESS for a two-arm Gaussian trial: 2σ²_obs / σ²_prior.""" + return 2 * sigma_obs**2 / prior.sigma**2 + + +pd.DataFrame( + { + "prior_mu": [p.mu for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR]], + "prior_sigma": [ + p.sigma for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR] + ], + "analytical_ESS": [ + analytical_ess(p, SIGMA_OBS) + for p in [INFORMED_PRIOR, EFFECT_PRIOR, FLAT_PRIOR, SCEPTICAL_PRIOR] + ], + }, + index=["Informed", "Default", "Flat", "Sceptical"], +).round(1) +``` + +```{code-cell} ipython3 +def simulation_based_ess(prior, sigma_obs, N_grid, n_sims, rng): + """ + Estimate prior ESS via simulation: find N* where the mean posterior variance + under a flat reference prior crosses the prior variance. + + Uses the same prior-predictive sampling as the assurance loop. Replace + gaussian_posterior_delta with an MCMC posterior to extend to non-conjugate models. + """ + flat_ref = EffectPrior(mu=0.0, sigma=10 * sigma_obs) + target_var = prior.sigma**2 + records = [] + for N in N_grid: + N = int(N) + seed = int(rng.integers(2**31 - 1)) + pp = pm.sample_prior_predictive( + n_sims, model=gaussian_generative_model(N, prior), random_seed=seed + ) + y_A = pp.prior["y_A"].values.reshape(n_sims, N) + y_B = pp.prior["y_B"].values.reshape(n_sims, N) + d_hat = y_B.mean(axis=1) - y_A.mean(axis=1) + _, post_sd = gaussian_posterior_delta(d_hat, N, sigma_obs, flat_ref) + records.append({"N": N, "mean_post_var": float(np.mean(post_sd**2))}) + df = pd.DataFrame(records) + post_vars = df["mean_post_var"].values + N_vals = df["N"].values.astype(float) + # post_var decreases with N; interpolate to find where it crosses the prior variance + ess_sim = float(np.interp(target_var, post_vars[::-1], N_vals[::-1])) + return ess_sim, df + + +N_ESS_GRID = np.unique(np.round(np.geomspace(10, 600, 30)).astype(int)) +N_ESS_SIMS = 200 +ess_rng = np.random.default_rng(RANDOM_SEED + 99) + +ess_results = {} +for name, prior in [ + ("Informed", INFORMED_PRIOR), + ("Default", EFFECT_PRIOR), + ("Flat", FLAT_PRIOR), + ("Sceptical", SCEPTICAL_PRIOR), +]: + ess_a = analytical_ess(prior, SIGMA_OBS) + ess_s, df_curve = simulation_based_ess(prior, SIGMA_OBS, N_ESS_GRID, N_ESS_SIMS, ess_rng) + ess_results[name] = { + "prior": prior, + "ess_analytical": ess_a, + "ess_sim": ess_s, + "curve": df_curve, + } + +pd.DataFrame( + { + "prior_sigma": {n: v["prior"].sigma for n, v in ess_results.items()}, + "analytical_ESS": {n: round(v["ess_analytical"], 1) for n, v in ess_results.items()}, + "simulation_ESS": {n: round(v["ess_sim"], 1) for n, v in ess_results.items()}, + } +) +``` + +```{code-cell} ipython3 +fig, axes = plt.subplots(1, 2, figsize=(20, 5)) + +# Left: ESS crossing picture for the default prior +res = ess_results["Default"] +curve = res["curve"] +prior_d = res["prior"] +ess_a_d = res["ess_analytical"] +ess_s_d = res["ess_sim"] + +axes[0].plot( + curve["N"], + curve["mean_post_var"], + marker="o", + color="C0", + markersize=4, + label="Mean posterior variance (flat prior)", +) +axes[0].axhline( + prior_d.sigma**2, + color="C3", + linestyle="--", + label=rf"Prior variance $\sigma_0^2$ = {prior_d.sigma**2:.2f}", +) +axes[0].axvline( + ess_a_d, + color="C2", + linestyle=":", + linewidth=2, + label=f"Analytical ESS = {ess_a_d:.0f}", +) +axes[0].axvline( + ess_s_d, + color="C3", + linestyle=":", + linewidth=2, + alpha=0.7, + label=f"Simulation ESS ≈ {ess_s_d:.0f}", +) +axes[0].set_xlabel("N per arm") +axes[0].set_ylabel("Mean posterior variance under flat prior") +axes[0].set_title(r"ESS crossing: default prior ($\sigma_0 = 0.5$)") +axes[0].legend() + +# Right: assurance curves with ESS positions annotated +for name in ["Informed", "Flat", "Sceptical"]: + res = ess_results[name] + df = prior_comparison[name] + ess_a = res["ess_analytical"] + axes[1].plot( + df["N"], + df["assurance"], + marker="o", + linewidth=2, + label=f"{name} (ESS ≈ {ess_a:.0f})", + ) + axes[1].axvline(ess_a, linestyle=":", alpha=0.35) + +axes[1].set_xscale("log") +axes[1].xaxis.set_major_formatter(mticker.FuncFormatter(lambda x, _: f"{int(x):,}")) +axes[1].set_xlabel("Sample size per arm") +axes[1].set_ylabel("Assurance") +axes[1].set_title("Assurance curves with ESS marked") +axes[1].legend(); +``` + +The left panel is a calibration check. The simulation curve, posterior variance under a flat prior as a function of N, crosses the prior variance at the point the analytical formula predicts. The two estimates agree to within interpolation noise. For non-conjugate models where no closed form for the posterior variance exists, the same loop with MCMC posteriors in place of `gaussian_posterior_delta` gives the correct ESS. The conjugate case validates the simulation approach before the closed form disappears. + +The right panel reads the ESS against the assurance curves. The dotted vertical lines mark each prior's ESS on the sample-size axis. An ESS of 356 (Informed) means the prior carries more information than 350 subjects per arm before the first participant is enrolled; the curve climbs steeply early because the prior is already doing most of the work. An ESS of 14 (Flat) means the prior contributes almost nothing, and every observation earns its full weight. The ESS converts the abstract question "how informative is this prior?" into a number on the same axis as the assurance curve: experiments whose planned N falls well below the ESS are prior-dominated; those well above it are data-dominated. + +This is the quantitative form of the trade-off the sensitivity analysis in {ref}`sensitivity_confounding` interrogates from the other side. There, the question is what happens when that committed information meets an identification gap, and the tipping point at which the conclusion turns measures how much that committed ESS has put at risk. + ++++ + +The three curves disagree most where they should: at small sample sizes where the data has not yet overwhelmed the prior. The informed prior reaches high assurance fastest because it is willing to commit to a narrow effect range; the sceptical prior assumes a smaller effect and so needs more data to detect it; the flat prior carries enough probability mass over zero that even moderate datasets do not push the posterior reliably above the decision threshold. The point is to make the dependence of the assurance number on the prior commitment visible, so the prior becomes a subject of negotiation rather than a hidden choice. + +## Planning as a posterior over future posteriors + +The experiment we have not yet run is a posterior we have not yet computed. What we have is a prior, a model, and the patience to ask what the experiment will likely say. + +Statistical power questions answers a conditional: given a specific effect, what probability of detection? Bayesian assurance answers a marginal question: given everything currently believed, what probability that the inference about to be drawn will be useful? The operation that produces assurance is the same one that will produce the posterior at the end of the experiment - only the data are still hypothetical. Assurance makes explicit the assumption power leaves buried, a believed distribution of effects, and derives from that assumption a posterior to evaluate. + +The Gaussian case and the Bernoulli case ran the same inference machinery. What changed was the likelihood, and with it the ceiling its geometry sets on how much assurance any sample size can buy. The next notebook, {ref}`sensitivity_confounding`, keeps the machinery and changes the question: not what an experiment will probably say, but what it did say once clean identification is itself in doubt. + +## Authors + +- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026. + +## References + +:::{bibliography} +:filter: docname in docnames +::: + +## Watermark + +```{code-cell} ipython3 +%load_ext watermark +%watermark -n -u -v -iv -w -p pytensor,xarray +``` + +:::{include} ../page_footer.md +::: diff --git a/examples/causal_inference/experimentation_triptych.jpeg b/examples/causal_inference/experimentation_triptych.jpeg new file mode 100644 index 000000000..da7651995 Binary files /dev/null and b/examples/causal_inference/experimentation_triptych.jpeg differ diff --git a/examples/causal_inference/multiple_experiments_meta_analysis.ipynb b/examples/causal_inference/multiple_experiments_meta_analysis.ipynb new file mode 100644 index 000000000..b613f316d --- /dev/null +++ b/examples/causal_inference/multiple_experiments_meta_analysis.ipynb @@ -0,0 +1,2151 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "58b4b1c0", + "metadata": {}, + "source": [ + "(meta_analysis_experiments)=\n", + "# Multiple Experiments and Bayesian Meta-analysis\n", + "\n", + ":::{post} May 2026\n", + ":tags: experimentation, meta-analysis, hierarchical models, partial pooling, replication\n", + ":category: intermediate, reference\n", + ":author: Nathaniel Forde\n", + ":::\n", + "\n", + ":::{figure} experimentation_triptych.jpeg\n", + ":name: experimentation-triptych\n", + ":width: 100%\n", + ":align: center\n", + "\n", + "The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance:* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis:* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis (this notebook):* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery.\n", + ":::\n", + "\n", + "## The replication-as-evidence problem\n", + "\n", + "Eight quarterly A/B tests of the same checkout-flow redesign, run across eight markets, return eight different point estimates. Two cross the conventional significance threshold; the other six do not. The product manager asks the natural question, \"did it work?\", and gets two incompatible defaults depending on which colleague answers: vote-counting (\"four out of eight worked, so it's a wash\"), or pool-everything (\"the combined estimate is positive, so it works\"). Both are mistakes. The vote-count discards the magnitude information in each estimate; the pool-everything pretends the markets are exchangeable in a way the evidence does not support. The honest answer requires a model that estimates between-market differences rather than assuming them away.\n", + "\n", + "Each experiment speaks about one market. The hierarchy is what lets us hear all of them at once.\n", + "\n", + "This notebook builds that model. The hierarchical Bayesian meta-analysis treats each experiment as a noisy estimate of its own market's true effect, and treats the per-market effects as draws from a population whose mean and variance are themselves the quantities of substantive interest {cite:p}`borenstein2009meta`, {cite:p}`higgins2009meta`. The structure is the one Rubin used for the 8-schools problem in 1981 {cite:p}`rubin1981estimation`, {cite:p}`gelman2013bayesian`, transposed to product experimentation. We develop it on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the third of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`sensitivity_confounding` for the interpretation counterpart. Readers wanting a deeper view of the partial-pooling vocabulary should also consult the existing PyMC notebooks on {ref}`multilevel_modeling` and {ref}`hierarchical_partial_pooling`, which we treat as predecessors rather than re-derive.\n", + "\n", + ":::{admonition} Where this lands in regulatory practice\n", + ":class: note\n", + "\n", + "The hierarchical model here is the borrowing mechanism a regulator now describes by name. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials presents subgroup analysis through a *one-way Bayesian hierarchical model* whose subgroup estimate is \"a weighted average of its raw estimated treatment effect ... and the overall estimated treatment effect\" {cite:p}`fda2026bayesian`, the shrinkage picture this notebook builds. The same guidance treats hierarchical models as the main way to borrow information across related trials by assuming the group parameters are drawn from a common distribution, which is the $\\theta_k \\sim \\mathcal{N}(\\mu, \\tau)$ structure below. Borrowing across studies, and the use of one trial's synthesis as the next trial's prior, is the regulatory form of the lifecycle loop these three notebooks trace.\n", + ":::" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d5b9bd7c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:26.257378Z", + "iopub.status.busy": "2026-06-01T17:59:26.257190Z", + "iopub.status.idle": "2026-06-01T17:59:28.475465Z", + "shell.execute_reply": "2026-06-01T17:59:28.474917Z" + } + }, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pymc as pm\n", + "\n", + "from scipy import stats\n", + "\n", + "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", + "warnings.filterwarnings(\"ignore\", category=UserWarning)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b8567665", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.477124Z", + "iopub.status.busy": "2026-06-01T17:59:28.476950Z", + "iopub.status.idle": "2026-06-01T17:59:28.791069Z", + "shell.execute_reply": "2026-06-01T17:59:28.790305Z" + } + }, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = 'retina'\n", + "az.style.use(\"arviz-variat\")\n", + "rng = np.random.default_rng(11)\n", + "RANDOM_SEED = 11" + ] + }, + { + "cell_type": "markdown", + "id": "ebedae74", + "metadata": {}, + "source": [ + "## Heterogeneity is not new: groups within a single study\n", + "\n", + "The across-study problem looks novel, but its structure appears inside a single experiment whenever the treatment effect varies across user segments. It is worth meeting the problem on this familiar ground first, because the tool that solves it here is the tool we will carry across studies, and its classical name is the analysis of variance.\n", + "\n", + "Consider one market's experiment broken out across six user segments. The redesign helps some segments more than others, and the per-segment treatment effects are themselves draws from a population. We give the section its own random generator so the across-study results later in the notebook are unaffected." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "409b8357", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.792839Z", + "iopub.status.busy": "2026-06-01T17:59:28.792614Z", + "iopub.status.idle": "2026-06-01T17:59:28.801581Z", + "shell.execute_reply": "2026-06-01T17:59:28.801048Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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segmenttreatmentrevenue
0New / mobile115.883319
1New / mobile014.339618
2New / mobile07.025209
3New / mobile013.596865
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" + ], + "text/plain": [ + " segment treatment revenue\n", + "0 New / mobile 1 15.883319\n", + "1 New / mobile 0 14.339618\n", + "2 New / mobile 0 7.025209\n", + "3 New / mobile 0 13.596865\n", + "4 New / mobile 1 11.434889" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "seg_rng = np.random.default_rng(2024)\n", + "\n", + "SEG_NAMES = [\n", + " \"New / mobile\",\n", + " \"New / desktop\",\n", + " \"Returning / mobile\",\n", + " \"Returning / desktop\",\n", + " \"High-value\",\n", + " \"Reactivated\",\n", + "]\n", + "N_PER_SEGMENT = np.array([600, 600, 900, 900, 1400, 1400]) # visitors per segment\n", + "SEG_MU, SEG_TAU = 0.30, 0.50\n", + "BASELINE, SIGMA_OBS = 10.0, 4.0\n", + "\n", + "\n", + "def simulate_within_study_segments(seg_names, N_per_seg, seg_mu, seg_tau, baseline, sigma_obs, rng):\n", + " true_effects = rng.normal(seg_mu, seg_tau, size=len(seg_names))\n", + " rows = []\n", + " for name, N_seg, eff in zip(seg_names, N_per_seg, true_effects):\n", + " treat = rng.integers(0, 2, size=int(N_seg))\n", + " revenue = baseline + eff * treat + rng.normal(0, sigma_obs, size=int(N_seg))\n", + " rows.append(pd.DataFrame({\"segment\": name, \"treatment\": treat, \"revenue\": revenue}))\n", + " return pd.concat(rows, ignore_index=True), true_effects\n", + "\n", + "\n", + "study_df, seg_true_effects = simulate_within_study_segments(\n", + " SEG_NAMES, N_PER_SEGMENT, SEG_MU, SEG_TAU, BASELINE, SIGMA_OBS, seg_rng\n", + ")\n", + "study_df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "8cd8bfc3", + "metadata": {}, + "source": [ + "The per-segment treatment effect is a difference of arm means; its standard error follows from the within-arm variances." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c85af685", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.802786Z", + "iopub.status.busy": "2026-06-01T17:59:28.802709Z", + "iopub.status.idle": "2026-06-01T17:59:28.810985Z", + "shell.execute_reply": "2026-06-01T17:59:28.810545Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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segmentdse
0New / mobile0.6140.338
1New / desktop0.8690.334
2Returning / mobile1.2430.251
3Returning / desktop-0.3390.268
4High-value-0.9120.215
5Reactivated0.2290.212
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" + ], + "text/plain": [ + " segment d se\n", + "0 New / mobile 0.614 0.338\n", + "1 New / desktop 0.869 0.334\n", + "2 Returning / mobile 1.243 0.251\n", + "3 Returning / desktop -0.339 0.268\n", + "4 High-value -0.912 0.215\n", + "5 Reactivated 0.229 0.212" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def segment_effect_estimates(df):\n", + " recs = []\n", + " for name, g in df.groupby(\"segment\", sort=False):\n", + " t = g.loc[g.treatment == 1, \"revenue\"]\n", + " c = g.loc[g.treatment == 0, \"revenue\"]\n", + " recs.append(\n", + " {\n", + " \"segment\": name,\n", + " \"d\": t.mean() - c.mean(),\n", + " \"se\": np.sqrt(t.var(ddof=1) / len(t) + c.var(ddof=1) / len(c)),\n", + " }\n", + " )\n", + " return pd.DataFrame(recs)\n", + "\n", + "\n", + "seg_est = segment_effect_estimates(study_df)\n", + "seg_est.round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "e1511edd", + "metadata": {}, + "source": [ + "The classical question \"does the effect differ across segments?\" is a test for the treatment-by-segment interaction, and the two-way analysis of variance answers it with an $F$-test. We compute it directly, as a comparison of nested least-squares fits, which keeps the dependency surface small and makes the variance decomposition explicit. The interaction row is the one to read." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "96f71013", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.812151Z", + "iopub.status.busy": "2026-06-01T17:59:28.812080Z", + "iopub.status.idle": "2026-06-01T17:59:28.823830Z", + "shell.execute_reply": "2026-06-01T17:59:28.823172Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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sum_sqdfFPR(>F)
C(segment)402.2605.05.0570.00
C(treatment)23.8881.01.5020.22
C(segment):C(treatment)828.4515.010.4150.00
Residual92081.3615788.0NaNNaN
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" + ], + "text/plain": [ + " sum_sq df F PR(>F)\n", + "C(segment) 402.260 5.0 5.057 0.00\n", + "C(treatment) 23.888 1.0 1.502 0.22\n", + "C(segment):C(treatment) 828.451 5.0 10.415 0.00\n", + "Residual 92081.361 5788.0 NaN NaN" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def anova_two_way(df, outcome, factor, treatment):\n", + " \"\"\"Type-II two-way ANOVA via nested least-squares fits (treatment is binary).\"\"\"\n", + " y = df[outcome].to_numpy(dtype=float)\n", + " n = len(y)\n", + " ones = np.ones((n, 1))\n", + " A = pd.get_dummies(df[factor], drop_first=True).to_numpy(dtype=float) # factor dummies\n", + " B = pd.get_dummies(df[treatment], drop_first=True).to_numpy(dtype=float) # treatment dummy\n", + " AB = A * B # interaction columns\n", + "\n", + " def fit(*blocks):\n", + " X = np.hstack([ones, *blocks])\n", + " beta, *_ = np.linalg.lstsq(X, y, rcond=None)\n", + " resid = y - X @ beta\n", + " return float(resid @ resid), np.linalg.matrix_rank(X)\n", + "\n", + " rss_full, k_full = fit(A, B, AB)\n", + " rss_add, k_add = fit(A, B)\n", + " rss_A, k_A = fit(A)\n", + " rss_B, k_B = fit(B)\n", + " df_resid = n - k_full\n", + " mse = rss_full / df_resid\n", + "\n", + " terms = {\n", + " f\"C({factor})\": (rss_B - rss_add, k_add - k_B),\n", + " f\"C({treatment})\": (rss_A - rss_add, k_add - k_A),\n", + " f\"C({factor}):C({treatment})\": (rss_add - rss_full, k_full - k_add),\n", + " }\n", + " rows = [\n", + " {\n", + " \"sum_sq\": ss,\n", + " \"df\": float(dof),\n", + " \"F\": (ss / dof) / mse,\n", + " \"PR(>F)\": stats.f.sf((ss / dof) / mse, dof, df_resid),\n", + " }\n", + " for ss, dof in terms.values()\n", + " ]\n", + " rows.append({\"sum_sq\": rss_full, \"df\": float(df_resid), \"F\": np.nan, \"PR(>F)\": np.nan})\n", + " return pd.DataFrame(rows, index=list(terms) + [\"Residual\"])\n", + "\n", + "\n", + "anova_tbl = anova_two_way(study_df, \"revenue\", \"segment\", \"treatment\")\n", + "anova_tbl.round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "398b3030", + "metadata": {}, + "source": [ + "The interaction $F$-test reports whether heterogeneity is detectable; it does not estimate how large it is.\n", + "\n", + ":::{admonition} Three numbers for heterogeneity\n", + ":class: note\n", + "\n", + "Given per-group effect estimates $\\hat d_k$ with standard errors $s_k$ and inverse-variance weights $w_k = 1/s_k^2$:\n", + "\n", + "- **Cochran's $Q$** measures how far the estimates spread beyond what sampling noise alone would produce. It is $Q = \\sum_k w_k (\\hat d_k - \\bar d)^2$, where $\\bar d$ is the precision-weighted mean, and it is simply the inverse-variance-weighted version of the between-groups sum of squares from ANOVA. If every group shared one true effect, $Q$ would follow a $\\chi^2$ distribution with $K-1$ degrees of freedom, so a $Q$ much larger than $K-1$ is evidence of real heterogeneity.\n", + "- **$I^2 = \\max\\!\\big(0,\\, (Q - (K-1))/Q\\big)$** rescales $Q$ onto the unit interval: the share of the total variation in the estimates due to genuine between-group differences rather than sampling error. $I^2 = 0$ means the spread is all noise; $I^2 = 0.9$ means most of it is real.\n", + "- **The DerSimonian–Laird estimator** is the classical, non-Bayesian way to turn $Q$ into a point estimate of the between-group variance $\\tau^2$. It is a method-of-moments calculation, and once $\\hat\\tau^2$ is in hand the random-effects pooled mean re-weights each group by $1/(s_k^2 + \\hat\\tau^2)$ instead of $1/s_k^2$, so noisy groups count for less and no single precise group dominates.\n", + "\n", + "See {cite:p}`borenstein2009meta` for the full treatment and {cite:p}`higgins2009meta` for the random-effects model these statistics serve.\n", + ":::" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b06c639a", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.825435Z", + "iopub.status.busy": "2026-06-01T17:59:28.825309Z", + "iopub.status.idle": "2026-06-01T17:59:28.829010Z", + "shell.execute_reply": "2026-06-01T17:59:28.828657Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cochran's Q = 53.38 (df = 5, p = 0.000)\n", + "I² = 0.91 DerSimonian–Laird between-segment SD τ = 0.807\n" + ] + } + ], + "source": [ + "d = seg_est[\"d\"].values\n", + "s = seg_est[\"se\"].values\n", + "w = 1.0 / s**2\n", + "d_fixed = np.sum(w * d) / np.sum(w)\n", + "se_fixed = np.sqrt(1.0 / np.sum(w))\n", + "df_q = len(d) - 1\n", + "Q = np.sum(w * (d - d_fixed) ** 2)\n", + "p_Q = stats.chi2.sf(Q, df_q)\n", + "I2 = max(0.0, (Q - df_q) / Q)\n", + "C_dl = np.sum(w) - np.sum(w**2) / np.sum(w)\n", + "tau2_DL = max(0.0, (Q - df_q) / C_dl)\n", + "w_re = 1.0 / (s**2 + tau2_DL)\n", + "mu_DL = np.sum(w_re * d) / np.sum(w_re)\n", + "se_DL = np.sqrt(1.0 / np.sum(w_re))\n", + "\n", + "print(f\"Cochran's Q = {Q:.2f} (df = {df_q}, p = {p_Q:.3f})\")\n", + "print(f\"I² = {I2:.2f} DerSimonian–Laird between-segment SD τ = {np.sqrt(tau2_DL):.3f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "04a75e3b", + "metadata": {}, + "source": [ + "The hierarchical Bayesian model is the same random-effects analysis of variance, with one difference that matters when the number of groups is small: it returns a posterior over $\\tau$ rather than a single number. With only six segments $\\tau$ is weakly identified, and the DerSimonian–Laird point estimate can collapse toward zero even when real heterogeneity is present; the posterior shows that uncertainty honestly instead of hiding it in a point." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "378cc883", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:28.830087Z", + "iopub.status.busy": "2026-06-01T17:59:28.830019Z", + "iopub.status.idle": "2026-06-01T17:59:31.101593Z", + "shell.execute_reply": "2026-06-01T17:59:31.101024Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "NUTS[nutpie]: [mu, tau, offset]\n" + ] + } + ], + "source": [ + "coords_seg = {\"segment\": SEG_NAMES}\n", + "with pm.Model(coords=coords_seg) as segment_model:\n", + " mu = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n", + " tau = pm.HalfNormal(\"tau\", sigma=1.0)\n", + " offset = pm.Normal(\"offset\", mu=0.0, sigma=1.0, dims=\"segment\")\n", + " theta = pm.Deterministic(\"theta\", mu + tau * offset, dims=\"segment\")\n", + " pm.Normal(\"d_obs\", mu=theta, sigma=s, observed=d, dims=\"segment\")\n", + " idata_seg = pm.sample(\n", + " draws=2000,\n", + " tune=2000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "500ed2c0", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:31.103366Z", + "iopub.status.busy": "2026-06-01T17:59:31.103256Z", + "iopub.status.idle": "2026-06-01T17:59:31.111420Z", + "shell.execute_reply": "2026-06-01T17:59:31.110822Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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pooled effectse / sdbetween-segment τ
Fixed-effect ANOVA (complete pooling)0.1480.1050.000
Random-effects ANOVA (DerSimonian–Laird)0.2700.3480.807
Hierarchical Bayes (partial pooling)0.2380.3550.872
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" + ], + "text/plain": [ + " pooled effect se / sd \\\n", + "Fixed-effect ANOVA (complete pooling) 0.148 0.105 \n", + "Random-effects ANOVA (DerSimonian–Laird) 0.270 0.348 \n", + "Hierarchical Bayes (partial pooling) 0.238 0.355 \n", + "\n", + " between-segment τ \n", + "Fixed-effect ANOVA (complete pooling) 0.000 \n", + "Random-effects ANOVA (DerSimonian–Laird) 0.807 \n", + "Hierarchical Bayes (partial pooling) 0.872 " + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mu_post = idata_seg.posterior[\"mu\"]\n", + "tau_post = idata_seg.posterior[\"tau\"]\n", + "comparison = pd.DataFrame(\n", + " {\n", + " \"pooled effect\": [d_fixed, mu_DL, float(mu_post.mean())],\n", + " \"se / sd\": [se_fixed, se_DL, float(mu_post.std())],\n", + " \"between-segment τ\": [0.0, np.sqrt(tau2_DL), float(tau_post.mean())],\n", + " },\n", + " index=[\n", + " \"Fixed-effect ANOVA (complete pooling)\",\n", + " \"Random-effects ANOVA (DerSimonian–Laird)\",\n", + " \"Hierarchical Bayes (partial pooling)\",\n", + " ],\n", + ")\n", + "comparison.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "1988dd9b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:31.112820Z", + "iopub.status.busy": "2026-06-01T17:59:31.112725Z", + "iopub.status.idle": "2026-06-01T17:59:32.155462Z", + "shell.execute_reply": "2026-06-01T17:59:32.154952Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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GydTUVLnqqqtk/fr1nqQN7grc3bp1k/vvv1+OHj3qi3vvueeekzvuuEOOHTsmfqIN3Jdddpls3bo10UmJCxOeRV4xLW8o8gfc0nfPO++8E5cLqe+T2267TX788UdPj8s7NPEuuOCCQAWJOd3XaXCZ22tkWh437fs6lZaWZk8i8Omnn8btfDqoY9euXRI2JtSLTbqv9Hg33HCDq0EZ0dC6R6tWreyOpCDTQTBt2rSxB8HFkgaKXX/99f+Y/GTUqFHyn//8R+LhiSeekOnTp3t6TJPuLzd4b4WX20netHzx559/epYenJqWGzWA2guxGHgca/p8DlpQd40aNVwFYcZDUPo7aT81611N2Sy2TKg/w9+0vqN9DPEa/KcThmm77rJlyyReChQoYE+i4pRXkwOc+B5108aiQW+IDM9Ybzz++OP2YG+nNL/rREPR0LqGtjk5lS9fPrt9LGvWrBIEJuRV08qUtKlHj/Z0d0y7x0yuo/uZCe8zr9vltB4Wy4DFoKTPKwSJ4X969uwp06ZN44qEwPjx4x3tV6JECalYsaKYRqP13XIy05Ku5HfxxRfbs5n6kc7YedFFF8nSpUtdHUdnGjjVDM6IP13FxY8Bwe+//77cc8894ic6e5MpMziY8izyikl5Q5E/4Nbbb78ddUeHW9rIp41Zy5cv9+yYvEMTz00AlJOALZ01648//nB8zs2bNzt6d7kJTHNzjUzL46Z9X6duvfVW+eabb+J6zo0bN8rTTz8tYWNCvdik+0oHgnz99dcSTxooprOYawBUUN18882yePHiuJxL38H6OykNDNHnWbw6bbSj895777U7ob1i0v3lBu+t8KpQoYLr9n9drV4HhsQ6UNV0AwYMcDyh3oni/Z71arKrWK5WGQsNGzYUvwtCfyftp+a9qymbxZYJ9Wf42wsvvCCffPJJXM+pQVLt2rWzJ6qMl65duzreV9uwvVwhfMyYMXZd2om6devaqyMhMjxjvZGcnCzDhw93NaHJo48+GvF9pP2eHTp0cDx5gnr33XelUqVKEhQm5FXTypS0qUeP9nR3TLvHTK6j+5kJ77OMVl912h8aj2vW3Ofp8wpBYvgfrXRrpSJonRj4N6eDGevVq2fc5dSGNi8itXXWlWjojABXXnmlzJo1S/xMX2oanKEzWDmxc+dOu2MYiaeNTO+99574lc449uyzz4offPjhh4EciOCEKc8ir5iUNxT5A16I14oNpxqgoyt8eDErFO9Qf6hTp44UK1bM0b66IqXOthYNDZ4+dOiQuOFkVTCnQWI6ENPpzJWm5XHTvq8bI0eOTMh5dfXJtWvXSliYUC826b76/vvv5aWXXpJEDT5/4403JKjGjh0b92fJvHnz7Jkp493e/ddff8nnn3/uybFMur/c4r0VXvXr1/ek/0sHhlSpUsUuNw8aNEgWLlwYqFk/g6BWrVp2G55b2mezbt06CZLZs2dL0AQhSMzv/Z20n5r3rqZsFlsm1J/hb1OnTpXevXsn5NwaLPLmm2/G7Xy1a9d2tRKSl6uJuak/s4pY5HjGeqtUqVL22AGnk2Ro/1PHjh0jWk2mV69eruobt99+u91nGhQm5FXTypS0qTtDe7pzpt1jJtfR/cyE91ms2uamT58upqfPKwSJ4R9WrFgR6MEG+G9npw6AcMLEILEJEyZ4soRrtLOZauPizz//LEGwZs0au3HCSYe5zp4T5Fmuw0Jn3+rXr5/4nTZuTZw4MdHJkO7du4spTHkWecWkvKHIH/CC09kfvaCrRrh9//EO9Q/taGvVqpWjfbW8P2XKlLit6OX0GLrqia6g6XTgbOHChaPez7Q8btr3Darjg7jDIuz1YpPuKw1Cv+uuuxJaJ0lNTU3YuYNGA8N0JsBly5Yl5Pwvv/yy62OYdH8FWdjeW36kA1jz58/vybF0lb9ff/1VHnjgAfu4WoZu27atnY+//fZbezZbuKMDEL0wbdq0wH1vLSO43fTZn5GaNWt6ch7d/N7WGYT+TtpPzXpXUzaLvbDXn+H/OuRtt92W0D6NeJ/bzWpiH330kScTsugEob/88oujfbNlyya33HKL6zSYgmes9y699FJXZWodYKwrjGQWvNq/f39XE3kErc0i7HnVtDIlberBEYb2dBPvsSAypT097O+zSALqCxUq5GjfeCx2UMrn6fMKQWI+kj17dmnSpInce++99iyGGkWvs47qjHl79uyxlw3WwW1aeNqyZYssXrxYvvvuO3n11VflmmuukQIFCniSDq1ceDHjPiRhswo7XWJal2I3jVcFzMqVK0f8Wa3Ev/DCCxIk+jx66623ot4vsw7NzJZo11lHNaJeGwY1iFWfhVop0cKiPgu1015nzNFn4cCBA+3leBs1amQ/T/FfOuOqFzNo6cDsSy65RF5//XX73bR582Z7cJo23B6fzbxly5auzqEd07qU8a5duxL682k+M4FJzyKvmJI3FPkDYdG3b1/HsxDxDvWfCy64IG4BW14EiUW7kpiTlcfcXBvT8rhp3zcMDedeTOjiB2GuF5t2X/Xp00c2bNjgKh2Ir0R2wOmqpLpKkVOm3V9BF6b3lh+lpKTY+TgWNN9qe9Mzzzwjl19+uZQuXdruINb/rf9N/7Zjx46YnDusLr74Yk/KITNmzBATZbZCQIMGDcQUfu/vpP3UrHc1ZbP4CHP9Gf6neUIn8TKJlnnLly/vaN9t27bJ119/7cl97zQ4rl27dlKkSBHXaTAFz9jY0CCvs846y1V745w5c075twMHDtjtLU7LMDlz5pRRo0ZJrly5JEjCnFdNLFPSph4sQW5PN/UeCyoT2tPD/D6LdftcvIKw6vo8fZ6wAqJ8+fI6Rasvt6FDh0b0HUqXLv2vfatUqWI9/PDD1i+//GKlpqa6ukZHjx6106LHdPudRo0a5Sotbs7dsWNHywt6HKdp0PwWVO+++67j7/3XX38F4n726vcZMmSIJ8+AEiVKRHzOY8eOWWeeeaZnz58GDRpYzz//vDV9+nRr7dq11uHDh62tW7dac+fOtd5//33r4osvtlJSUjw5V8GCBa0dO3ZE/F01LdmzZ3d0roYNG1oLFy50+Mta1pEjR6wpU6ZYzz33nHXeeedZWbJkOeV5evXqFfr3z7XXXuv6PBdddJG1YMGCiK79Tz/9ZFWoUMHV+f7zn/9Ybujvmujf5sStW7duMU2vEyY9i4KcNxIl7PlDy92J/u1P3jRNfhWr+0brRnoPfPrpp9Zvv/1mzZkzxxo/frz1wQcfWNdff72VO3duz851xx13OPruYX2HBrlss3LlSsfHbt68ecS/fVpampUvXz5PvtOqVasiPu/NN9/s+Dzff/+9Fa2w5nG+b+yf4fnz57c6depkffzxx9bPP/9sP8N/+OEHq3///latWrWMeD+aVi8+HZOeIxs2bHD8W55qK1WqlJ0WbYP9/fff7fto3LhxdrveZZddZmXLli0m92807yUv21pPt+n3vPrqq60PP/zQfp5oHWHixIn286ROnToxuQYnbk2bNrVeffVV+xmmv4GWS9944w2rcePGnhy/d+/ejq+3SfeXSe+tIJfFE01/s0Ren2rVqlm33367NXLkSGvbtm0JuQZ+6VeJRLNmzVxf8yuvvNIykZYDMrouAwYMsEzh5/7OsLefmvyuPh0Ty2bxFpb6c9DLe6aO89mzZ4/9LPLqWpctW9bq0aOH3f9xYp1/8ODBdhnHy/YFt3X+F1980dVzza0LL7zQ8fm/++471+c3RViesX4ab3GiZcuWWXnz5nV8/rp1655yzOidd97p6nu98847VtCEPa+aVqY0vU2d9vT4tqebeI+ZUEcPav0q7O+zSHXt2tXRNdA2sIMHDxqfPi8EJkhs+fLl1qJFi065TZgwwdXN+sILL5z22JFsu3fvjipITAskWgiYOnVqTK7Vvn37rHbt2rm6JldccYWrNJjaeOQHXbp0cfy9Dxw4YExn5jfffGNlzZrVVTqOb1rAjNSwYcM8OWfJkiWt0aNHR3RO7UQ666yzPDnvAw88EPF31QKz06C77du3W17SDq+PPvroXx1pkRR2gvz+0UqxFxWw9PT0qK735s2b7QKr03Pqvbl06VLLqaAFAiWi0dKkZ1GQ80aimJo//NKR4Dde3zc6EEUHAWf2btE6jTaIJScnuz6n1r+0EToaYX6HBrlsoypWrOg4Hxw6dCii32HWrFme5XnN75HSwQNOf3e9Z6IR5jzO943dM1zrUk8++WSm95J2yOXMmdP1+Z566ikr6MJSLz4V054jWsb04j7SIOS333470++9ZcsW67rrrvP0HvZbkFirVq2s9evXZzghWs+ePT2/BrqVKVPGDgg7Hf19tMPT7XnOPfdcR9fatPvLpPdW0MviiaT52ctBCG42rafq/a1BphrEES9+6FeJVPfu3V1f5zPOOMMykQ56y+i6aDC1Kfzc32lq+6kJ7+pTMbVsFm9hqT8Hvbxn6jifvn37evJcK1CgQET9H5rHOnTo4Mk53db59f5x+oxNSkpy1c6gky84DYLWMpNO9gaznrF+7tsdPny4qzQ88sgj/zje2LFjXR2vffv2VhCFOa+aWKY0vU2d9vT4taebeo+ZUEcPav0qzO+zaLz55puOf58ZM2YYnz4vhGIUo76IgzBDYqVKlezBwJs2bYr5uTQSVWeacHpN8uTJ42plM1Mbj/xAH+ZOB+ya0JmpL1G9D7XByk0aTty0sh+p+vXruz5fzZo1o56tVBvIrrnmGtfn1mdDpAMGdOYmLxo/vKaVwpdfftmqXr2668KO398/Tp8Hx7eHHnrI8bl1oFfRokUdn/uuu+5yfO5YBgJVrlzZnuVAG+W0QK8DQXTg2q5du6wVK1ZY3377rT0Tg1Zcjwei+jFIzKRnUZDzRqKYmj/81JHgJ17eNzrz+saNG6M6v66O5MWsX08//XRU5zX1Her3so3SleFiPWP0K6+84lm+v+222yI6p5tV0lq0aBH1dTQtj5v2fWPxDNeZUKdNmxbxubVh/nQzk0W6nX/++VbQhblebNJ9pR1iOtDL7X2kwcD6vI+Gzvjr1X3spyAxfZ/rChyZ0Q7ZSy65xNNroPk+0k62e++919W5dKZInbUxWibdXycy/b0VhLJ4orkdJBeLTeurOvguVpNCBjVIzIv3Vzz7rPxCy2iZXZedO3dapvBzf6ep7aemvqtNLZvFW5jrz0Eq75k4zkfrpk4n7zpx0/Fg69ati+rcOljTy3ErTuv8nTt3dnxOHUiciFVDH3vsMcfnNVHYn7F+6dvVVVfcTEaiq34oLSPqIHGnx9JVbfw+EYyJedW0MiVt6rSnx7M93cR7zOQ6ehDqV2F+n0Xjq6++cvz76KqRpqfPC6EYxejnm/3kqOF40uUs3VyXyZMnOz63iY1HflGjRg1H31mDCuMlXp2ZGuioL7Z58+ZZ77//vnXLLbdYOXLkcHXuk7fcuXNb+/fvjyg9OijVi5mOM5plObPgUV1C1G0atKAQiU8//dT3S567jbz38/vn77//dtWo3KhRo6hnxzjZyJEjHZ8/V65c9kwGTsQiEEgb9j///POo0qEd9oMGDbLeeOONmKY3WqY9i4KcNxLB5Pzht44Ev/DqvtFZHVevXu0oDZ988onr8+vqU5G+10x+h/q5bOPFtenTp09E59CVtb3I98eDiCOh187pOaJtwDMtj5v2fWPxDNfBz05WLNBBIm7OW6RIESvowlovNu2+cnOu41vhwoWtxYsXJ3RGc78EiWl5P5qOXi9mAD2+5c+f31qyZEnE59Z2RbczYur9Eg3T7q8Tmf7eCkJZ3A9uvvlmz54JXm8tW7a0VyWOlSAFiemEL15c00gCisNk3LhxmQ72NIlf+ztNbj818V1tctks3sJafw5aec/EcT76PHL7XNPny7Jlyxx93wEDBrg+v9s6/+zZsx2fs3Tp0o5X9LrgggscnzdIKyX6QdifsX7p29WxYzro2mk6qlSpYh/j6quvdnwMXSEkmkH+fhPWvGpimZI2ddrT49Webuo9ZmodPSj1q7C+z6I1c+ZMx79Pv379jE+fF5IFcVO8ePG4Xu1WrVq5Oufs2bM9TQ/iY+3atY72K126tATFmjVrJCkpKdMte/bs9j1Qr149uf3222X48OFy+PBhT9Nyxx13SO7cuSP67IgRI1yfb+DAgY5/K70eQ4YMkWzZsrlKw8iRIyP63JEjRxwdf/Xq1RIvhQsXlrAaNmyYtmY53v/111+37yM3rrvuOqlWrZqjfQ8ePCijRo0SP7jllltk0aJF0r59+6j2K1iwoHTr1k3uu+8+8RPTnkWxFLa8ocgfiJU333xTypcv72jfG2+8Ua6//npX51+1apXMmDEjos/yDvU3rec6LaP8/vvvmX5Gy0+TJ08Wr6xYsUI2bNiQ6ed+++03V9ckGqblcdO+byw8+eSTUecz9cADD0hKSorj827fvl127NghQRbWerFp99Xo0aPFrf79+0v16tUd7fvII49Is2bNJAyyZMkigwcPlqxZs0a8T/PmzSV//vyenP/xxx+PKt8UK1ZMWrdu7eqcixcvjurzpt1fscB7K9zefvttqV+/vvjRr7/+Ko0aNZIuXbrIgQMHxGRe9YfqM8Ukf/31V4Z/b9iwoZjEr/2dtJ+a9a6mbBY/Ya0/w/8+++wz18d46aWXpEqVKo727dmzp13vTaQzzjhDzjnnHEf7atv3999/H/V+27Zts8vPTmhaq1at6mhfU/GMjQ8dO6ZtIjoewonly5fb+XvMmDGO0/D8889L06ZNJajCmldNLFPSpu4N2tMjY+I9ZmodPSjC+j6LZxudxgiYnj4vECQWYsnJyVKrVi3H+8+bN8/T9CD2tm7d6rjTLEhBYn6RM2dOe6BOJNLT0+Wbb75xdb5zzz036kCEk2nj5P333+/qGLNmzZL169dn+rkcOXI4Ov77778vGzdudLQvvKlwN27cWJo0aeLJe8jNoP4vv/xSEu3ee++1K5NuA5r8wsRnUayELW8o8gdipWXLlnLllVe6OsaLL77ouFPluJ9++imiz/EO9TcdrF2nTh1H+/7xxx+SlpaW4Wf+/vvviBojdXB7pAMfIwlOcxoklitXrqg7/EzL46Z9X69pgO9DDz3kaN9ChQq5Hsga9LphWOvFJt1Xx44dk4kTJ4obeh906tTJ8f7aOfnaa6+57qT0g1tvvTXqgVz6W3sxKF7LEE7qoW6DxCIJFjf1/ooF3lvhlzdvXhk3bpzUrl1b/EgHpLzzzjty5pln2gP8TO478YJpQWKZTd5pUpCYX/s7aT81711N2Sx+wlp/hv+NHz/e1f46gYHWdd145ZVXJNG6du3qeF+dHDRaGgSjbS5OdO7c2dF+JuMZGz/6TBgwYEBCJvRv06aN43KWX4Q1r5pWpqRN3Tu0p0fGtHvM5Dp6UIT1fRYtHU/jNJAwHgFzxX2ePi8QJBZyJUqUCH2kI/6/TZs2Ob4cRYoU4VJGqU+fPlKyZMmIZ4DUTi23AQle0JlM3frxxx9jFm2us0bpQFedtSuzQbw4/SzVbgYhdOjQwdPAAKd09rBEzrqrM7V7MVuIn5j4LIqFMOYNRf5ArHTv3t31MSpUqCDt2rVzdYxIBnjzDg0GJzNZKS1X/Pnnn64DutRZZ50VcToyCwBbt26dvdqdEzqrZDQBy6blcdO+byxox4DThmxVt25dV+ffsmWLBFkY68Wm3Vc6MGPXrl3ihgYmaQehGxpscPbZZ0vQOa0HOl2F7UQ333yzHVwdrZo1a8btOWba/RULvLfM6feaNGmSXHjhheJXS5YssZ/bCxYsEBO5neTluNTUVDFJZgNCGzRoIKbwa38n7admvaspm8VXGOvP8L+VK1c6bpc97r777nNd5/dqcLIbV111leNA6++++y7qwaxOV3DTSSOuvfZaR/uajGdsfGlb4BVXXBH3erJOcBv08QthzKsmlilpU/cO7emZM/EeM7WOHiRhfJ85ofUkDSaMd9tgWNLnBYLEQs7N6hbRznKKxHNTUHAySMJkGiDQo0ePiD8/ffp018uSux0YfeIKPm6j+CP5PjqY2ykdKKuzK2i09g033CADBw60V//QCGydqREZmzp1asIqLafKb04dPXrUXi0qUbPdDh061HWjvt+Y+CzyWljzhiJ/IBby5csnF198sSfHuu6661ztr8FBOqt7RniHBsMFF1zgeN/MgsAiDRLTlTV18yJIzOkqYk6uhWl53LTv6zWdOcvts7dcuXKu9t+7d2/En9X6onaCx2uLZIawMNaLTbuv3Mzee3yQ/NVXXy1euOmmmyTISpUqZQdZO1GmTBnX53dal61UqVLcnmOm3V+mv7fgTsGCBe3Jg/r16+fZqlVe2759uz2Te5hmf43U4cOHPTmOm0EqQaPPjxUrVmT4GZNWEvNrfyftp2a9qymbxVcY68/wP7f1lixZstjBVV5IdOCTPqOdDkTXFWO07zRSOqGp0zZxfY9ofzWiwzM2/j744AMpW7ZsXM6l4xY+/vhjKVasmARdGPOqiWVK2tS9QXt6ZEy8x0ytowdJGN9nTjltu49X0GROn6fPLWfrpCFm9u/fL/Pnz7c3nbVm7dq1drDWzp077Vlr9+3bZ78QdIt1pKhGpSJY3Dx4/NqR6teXuC7xqo1+kZoxY4arc55//vmedmy1bdvWnvHQqUi+T8WKFaVAgQKye/dux+fRZ9+oUaPs7cQBVnrsqlWr/m/TGaV1ZgJWxHPfUZknTx6pVauWeMXtb6Lf5bzzzpN469ixo1SrVk3CxsRnkdfCmjcU+QOxoAPivJpBXJ8ZWv7SDkcntC6ls4JmNNCXd2gwaNlAGy2d1Ik1CExnxDodXZEgEhogFmnjns5gph3fp+ugizQwzYsgMdPyuGnf12vaMVK0aNGEfm+vBhgnShjrxabdV3PnznV1jubNm0v+/PnFCxrkpDMRB5VOHOB0NmO3v7XWY3X1TSf0Ho7Xc8y0+8trvLfMowPhHn74YXtA7eOPP27PsOq3jnINENMZiSdMmBD4Gd2jcfDgQU+OY9LkhnPmzMlwYhtdGUA3U/i1v5P2U7Pe1ZTN4iuM9Wf437x581ztr7P8e5WPLr/8cnnwwQclke666y559tlnHa3m+v7779tl8kjKvGPGjHHcz9O5c2dH+5mOZ2z86aoUI0aMsMdXOM3vkXr00Ud9vdK26XnVxDIlbereoD09MibeY6bW0YMkjO+zsAZh5fR5+twiSCzBtMNq8uTJ8s0338gvv/xidwL4pRPr0KFDiU4CQtJpEibly5eX8ePHRz0Dy7Jly1ydt379+uKlevXqudo/ku+jDYBacP3666/FS9ooqQNtdTvdLBpnn322PfinSZMm9gBi0yxatMhVsHI0AZCxtnDhwoQ1goeRic8ir4U1byjyB2KhQYMGnh1LB4fp7EtLlixxfAzdN6MgMd6hwVmhTst8f/zxR9T7av1b69ynWhFSn4ORzPKv+x4f9K8Np5FMsKKBYO3btz/l35zOmqqdjGeccUZU+5iWx037vl5r3Lix62PkzZvX1f46SVKQhbFebNp9pZN4uRHtczqzGRl15RydSCyItJPKKf3ebuhEH07vA7cBCtE8x0y7v7zGe8tc2jE+cuRIeeqpp2TQoEH2QDyvgpS88PPPP9vpC/qKkNHYtGmTJ8cxKUgss5nWTVpFzM/9nbSfmvWupmwWX2GsP8P/3PQ1eN1vqn0fWvZJZDlW27p11YJhw4ZFva9O0Ddx4sSIAlV0cgcnatSoIc2aNXO0r+l4xiaGvluefvpp6dWrV8zOofdEnz59JCzCmFdNLFPSpu4N2tMjY+I9ZmodPUjC+D4LaxBWTp+nz61/j4pCXOggMi2k69LC+jB4+eWX7ZU0/BIgpggSCx43DUYEiUU2yHnKlCl2BHa01qxZI4kq+MfieJrXtm/fnunn3C5JGy0d1KtBt4899pi0aNHCjpDXmWS/+OKL0M48EIv8Zvp30fvDy6AGPzH1WeSVMOcNRf5ALHj93Khdu7ar/XWV5ozwDg2OaFfQOk5na1qwYIGrFb208//4qjCRrkpyumNv3rxZli5dKk7oDJSnCnbLiGl53LTv6zUvglty587tav+MVlMIirDVi027r9avX5/QiTFifbx40sFciWq3dHNut6viRvMcM+3+8hrvLejMv++99579LtSVDFq3bi3ZsmXzxYXRQYFhKNdEat26da6PUbhwYaNWX8ssSCzMbZJB6u+k/dSsdzVls/gLW/0Z/pdZf0Gs+ytOpOWemjVrSqJ17drV8b6DBw/O9DNbt26NuB3+ZLfddpuj/fBfPGMT48knn7RXaokFnVRJJyTxwwBwL4Utr5pYpqRN3Ru0p0fGxHvM1Dp60ITtfRbvScDiNXlGLp+nzy2CxOJMb7bnnntOKlSoIL17945olvJESUtLS3QSEMeXZphfuF40yGlj2LRp06R06dJR769Lh+vgT7ezoXrJi+NFUqnT1RI0Sj1R9uzZYxd0tMCj6dBl1rds2SJhpsHGbhu0wzagIFq6MkgYmfws8kpY84YifyBWdPZLPx0vo/oX71AzgsTU6TqhI+2cPvfcc0/5vzNyutXCnK4iplq1ahXV503L46Z931jwYmBK1qxZxXRhqhebeF+5bUPQCcK8VKZMGQmqjFZzzUyOHDkSdu54MfH+8hrvLRynEzp07txZxo8fb08uNGbMGLt9X4NsEjU78PLly2XcuHHG/Eh///2362OUL19eTKITiWbEtJXE/NjfSfupWe9qymaJEab6M4LB7Xgtv/V/eEFXH2jatKmjfb/66qtMJ/ccPXq0/U6NlgbB3HrrrY7Shf/iGZsYOtHf8OHD7YHaXtPJUcqVKydhE6a8amqZkjZ1b9CenjlT7zET6+hBFKb3mRtO2+niteCS5fP0uUWQWBwtW7bMXsLvqaeeCkwUIYLFaVSrYuW40y/NPX36dHnttdcczxysS0u6fSnky5dPvKQzqLqdRVWX3I3kPM8//7z4wa5du6Rfv3524+pLL70UmBe1k/zmpGHVr7TAGm+NGjWSMDL5WeSVsOYNRf5ArBxfbckrbp9DGb1XeIcGr5zudHZwL4PEdGXwSMyfP98uj3oZJBZtoJxpedy07xsLBQoUcH0Mv6zekUhhqhebeF+5bcPNmzeveMnrOlk8uUm726AOr3+HWDDx/vIa7y2c7v6/6qqr7PZ9DcLRlYV//vln+93crl07KVasWNwu3Oeff27MjzRz5kzXx9DJNk2RmpoqixYtyvAzpgWJ+bG/k/ZTs97VlM0SI0z1Z5hRbwlrnd/pamJHjhyRjz76KMPPfPbZZ46Ofckll0iJEiUc7Yv/4hmbODoZ+dChQz095n333WfXdcMoTHnV1DIlbereoD09c6beYybW0YMoTO8zN5y207ldpS4s6XOLILE4mTNnjj3byrx58+J1ShjIj50mQZ3JpW3btjJhwgSZMmWK66AAL65tLAazuD1mpJW6Tp06ydVXXy1+oQElDz/8sFx66aV2ZSFswhaEnIjvU69ePQkj059FXghr3lDkD8RKnjx5fPXMyCiv8w4NFp3AwekKj5MmTTrlypSrV6+OaP9zzjnnH++GSBpQdQaiU53XaZCYdipWr149qn1My+Omfd9Y8GJgSqJW6/CbsNSLTbyv3JaTvR7g5ZcBY/HuMNG2Oj+VSWPBxPvLa7y3EOnz4Pzzz5fHH39cvvnmG3v21BUrVtgzu99xxx0xXb3hxx9/NOJH2rlzp8yePdv1cSpXriym0ElF0tLSTvv3ggULGhU059f+TtpPzXpXUzZLnLDUnxEMhw8f9lW/qV/qrrragNOArCFDhpz2b1r2jnSitpPpSsFwj2ds4lx22WXSrVs3T45Vq1YtefnllyXMwpJXTS1T0qbuDdrTM2fqPWZiHT2owvI+S0S+jlcQ1kGfp88tgsTitAxk69at7Y4RZM6rKFW3DTpB5MdOk6DQBrw2bdrIG2+8IRs3bpSxY8dGPTN/RjMmuZUjRw7xmtOVF06c3TJSw4YNszvf/UQ75S+//PIMO1+DKJrfJQgS8WwqXLiwhBHPIvfCmjcU+QN+LJ/GoqKd0XuSd2jwOC2vb968WZYuXeooWKtmzZpStGjRfwxajzRY7eRzbN++PdPZ4r387qblcdO+byx4MTAlKSnJk7SEQRjqxdxX8Q9uClOHWyI7TLwuk8YC95d7vLfgVKVKleTmm2+WwYMHy7Jly2TlypUyYMAAz1eU134H3cJO+1a8aHNv3LixmEJXuctIgwYNxDR+7O+k/dSsdzVls8QKQ/3ZREEc5+P2Xvdb/4dXsmbNKnfffbejfRcvXiyTJ08+5d9Gjx7tKJ/o6r86yTO8wTM2cXSyQi9s2LDBiLplGPIqZUpnaFP/L9rTucdiLUh19CALw/vMDaftdPHq1zvk8/S5RZBYjOls4TfccIM9+AvxbTyK9/KbQS8chi2y/uQBNPpQ1tkWtcP37LPPtpfd1qjoDz74QGbNmmUvqTlu3Dh7Se7ixYt7vsqBW7H4fdxGg0cTuKZ584cffpAuXbqIn/z888/Sp08fCRMv8pvf3qPxlj9/fgkjnkXuhTVvKPIHYsXrDl23A30yWu6ed2jwuJnU4eQZSyMNEjv33HP/9d/OO+88R+fU/99pWcfJdzctj5v2ff3aERfkgBavhaFebOJ95XbSHp2Vz0tBbu/0unM/KOeOlIn3l9d4b8ErFStWlJ49e8qMGTNk6tSpnk0mpxYuXChhl9HqEdFo2rSpmCKzlddMDBLzY38n7admvaspmyVWGOrPJgriOB8NhnLD68BkP03sfM899zi+Pjr5wql8/vnnjo7XoUMH178V/j+esYnx9ttv24GSXj0nb7zxxtAHLochr5papqRN3Ru0p2fO1HvMxDp6kIXhfZaIOk68AmUP+Tx9bvm/dzTgPv74Y7sTCfGdiU3t3bvXuMvudMl3FaRAxvLly9uFokg3rRhrQJSu5rdixQr7nhwzZoz069dPbrvtNjnzzDNjWmDxImp43759nqTFy2NG+720YP7WW2/Jr7/+KmeddZb4Rf/+/WXVqlUSFkGJUvczL5ZT9iOeRe6FNW8o8gdixesyjNvjZbSSKu/Q4NFyfIECBRztO2nSpAwDuKIJEjvVfzvdwL8T66mRBqadSqtWraLex7Q8btr3RTAEvV5s4n3l9jv7rSwE/zLx/gKCQCecmzBhgv2u9MK6deskzHRCvpPrWk6ULVtWypQpI6bILEisYcOGYho/9nfSfmoWymaJF/T6s4mCOM4no/6CREwM46c6v76L27dv72hfDQbbvXv3P/7bli1bIm6DP1nnzp0d7YfT4xkbX/Pnz5cePXp4eszp06fLk08+KWEX9LxqapmSNnUEJa8B8RL095lTx44ds8fsx7ttMCzp8wJBYjH2wgsveHIc7Qy599575dNPP7U7C7Zu3WoHvWQWHNOxY0cJGq+W2vVqmeYgKVmyZIarI2S2HDViVyBNSUnx1YxZGgHtdlYZpyvq6EoLM2fOlIkTJ8p1113negYRLxqsBw4cKGGhUerM0uCO2/vVr3gWuRfWvKHIH4gVvw2MzpMnz2n/xjs0eHR2q5YtWzra98QOaa1fL1myJKL9ThUQpsFqkcwUpI1MU6ZMcR0kVr16dUcDJk3L46Z9XwRLUOvFJt5XxYoVc7W/14OUN2/e7Onx4B8m3l9AkDz00EP2agpu7dq1S8JMV2DzwhVXXCGm0HrivHnzMvyMiUFifuzvpP3ULJTN/COo9WcTBXGcT968eX3V/+F10JlbXbt2dTwWZcSIEf/4b1988YWj1eaaNGkitWrVcpQOZI5nbOzpKrfXX3+9HD58OCYDu3/66ScxQVDzqqllStrUES+m3mMIrqC+z9z0aWrbp9OFZGJts8/T5wWCxGJo8uTJEQ80O53ChQvL+++/L6tXr5Y333zTrjicccYZUrRo0dBGQmvwm1sa3bl27VoxTVJSkpQrV87RvgSJxXbwaunSpV0dY9myZZ6lx6vj6WyebujqB6NGjbIH5epsUjoDVOXKlSURRo4c6fiF78f8VqpUqUQnAz7EswjkDySC17POaL3I7SCj0+EdGkwXXHCB47x0fBb/SGcwrVix4imDszSIuFmzZhEd4/i5dHCozh4Zr1XETMzjpn1fBFPQ6sUm3ldu23P+/vtv8VJmg8gRXCbeX0DQ9OnTx75X3dABs2GlfZlOV4c42TXXXCOmWLx4cYb5Qgc8VatWTUzjx/5O2tfNQtnMf4JWfzZREMf5uJ39fc2aNeKn/o9YrKrrdKWDwYMH/+P/1/vWCVYRiw+esbENtly0aFFMjq2LB3To0MF+N5oiaHnV1DIlbeqIF1PvMQRf0N5nTrlpo6tQoYLE2gafp88LBInF0Pfff++6wDRt2jT7AeA04tnr1YfiwYvZdubMmSOmchqhSpBYbDntzDrO6QDSWB1PVxFzupLYqWboat++vd2JvHz5cjtCW5+fffv2lVtvvdUecFu8eHGJJZ3Z+88//5SwcFMI0cbezFapjPcG7/AsAvkD8eZ1GWbBggUxbZTmHWpOkJg6PoAx0oGMp1pFLJK/nej46mGTJk1yNHOq2+9sWh437fsiuIJULzbtvtIAYb+UhbZt28ZKYiFn2v0FBHEmbF1F2A23QWZ+pUHMTleaONVg7XPOOUdMMXv27Az/Xr9+/dDmmyD2d9K+bhbKZv4UpPqzaYI4zsftIHa3/RWxnmjGC07LeHPnzpVZs2bZ/1vvU20Pj5ZOnH7DDTc4Oj+c4RnrrU8//VQ++OADiaUtW7bY7z/T2mGClFdNLFPSpo54MvEeQ3gE6X0W7za6eKzUtcHn6fNCSqITEGZOKrknz6xStWpV14MHEkFnUk9LS0tYmr/55hsxldOCts5kr8tch3WFukSrWbOmq2dCZh2F8W5grVGjhsSKFmwuueQSezt59jFdjWTFihX2Smg6244uv6qNpU4H2J5oxowZ0rhxYwkD/X2c5jdtzNZKh87UifDhWQTyB+LNy9Uujh496nql5szqV7xDg/lu0xnCNm7cGPW+Ghx28803xzVITDvGtd7ldIZ9HRx4/vnni1Om5XHTvq/ptCMoLB0ofq4Xm3Zf1atXz9X+U6ZMsX8bLwZ3//jjj66PAX8z7f4Cgkg7f/Xd61QY+1+0TNKmTRvPVkm77777HE+cGUSZ9f00aNBATOXH/k7a181C2SwY/Fx/DiLTxvm4HY/lZZDYunXrfDkJ+PXXXy8PPvigo99Xx7zpSmRffPGFo/tOV5fNly9f1PvBOzxjnVu5cqXcfffdEg/aZjhgwAB56KGHxFR+zqsmlilpU0c8mXiPIbz8/D5zYv369b5eqWu9z9PnBTOnHouTxYsXO963WrVq/7rRo6UvMH0gJEL27Nkd76uD+9w8uHTpQ52Nw1RuCtpu8iwy1qRJE1eXSAeR7ty507PL7LaB1e33cSJ37txSp04dueKKK+yGSI2g14HnGkH/5ptvup7BMVHPy1hw8/voLG86MwHCiWcRyB+IN+2Y8Gpp8p9//lmOHDnieP8cOXLY9ayM8A4NplatWjnaTxuMd+/eHfEqLxkFgmne0TwWSbCjrhh+fEWxaJ1xxhlSqFAhccq0PG7a90X4+aFebNp95XZgtrZzTp482ZO0fPLJJ54cB/5l2v0FREqDj/QZ6EWHt1tOB00fF7ZBrlOnTrVX/dKyiBdy5swpXbp0EZNkNqFfw4YNxVR+7O+kfd0slM2CzQ/15yAybZyP20HsWt/fv3+/J2n54YcfxK954q677nK078iRI+0BrZ9//rmj/Tt37uxoP8Qez9jM+4F0Fby9e/fGLTs+8cQTriY0CSs/5FUTy5S0qSOeTLzHYB4/vM/i2T6nE2/WrVtXYm2xz9PnhVAEibmdUc7NQMPT0RnKdBk+p7RTxS1dvnvr1q2SqGUQnUpNTXX18h01apS9nLKpdCYepyIdHInoNW3a1HUjwpgxYzybmXLp0qUJ/T5eKlq0qNx7773293Lz8nWyfKgf3z/Hl0N2w2lDLfyPZxHIH4g3LZc7DYY52Weffea6wzezd7fp71C/lm1iFSSmMyxpGTuSwQslS5aUKlWqZNhZHunsSmPHjnW8UvAFF1wgbpiWx037vjBXPOvFpt1X2s6WJ08eV8cYNmyY63ToDIE//fST6+PA30y7vxCOsng8aJ+RrgCsHeHa/5PIYDGdrdWNsmXLShhosFzfvn3tVY697I/TAciFCxcWk2TWL+d28HqQ+bG/k/Z1s1A2Cyf6lTNm2jgft8HYhw8flu+++86TtOhqW36lQfy6ypyTgdcDBw50NHlO5cqV5bzzzpNY0Zn/ddUQJ1vLli1jlq6gS+Qz1k8ee+yxuAdsJSIwLchoT48t2tQRT9TbzEV7uv/LXhrI5kT16tVd1U3Dkj4vJJs+m43atWuXeE0ru24UK1Ys4YMo3S576MYvv/ziaD+dpefhhx8Wk+nM8k4aaI4voYrYqFWrllSsWNHVMV577TVPVuJ49dVXXe2v+euiiy4Sv9EVFXQJdaeczPLlx/ePF/nt448/tlejRPjwLAL5A4nwzjvvuD6Grqg6evTomAcSmf4O9WvZJpaBUy+++KLrVcSi+YwaPHiw43K92yAx0/K4ad8XiEe92LT7KmvWrK4H/3z44Yeu29x69OjhevUa+J9p9xfCURaPJ53kQQe9aSfsG2+8Ya9KEE8LFy50HXhSvnx5CTJ9xugAZu2Hevzxxz0NTixSpIj06tVLTLJjxw7Ztm3baf+ug5D13WAqP/Z30r5uFspm4Ua/8qmZNs5H73O333nIkCGeTETg9NrFQ+nSpeWqq65ytG+fPn0cTfLQqVMnuyyEYErEM9Yvxo0bJ6+88orj/d2U/1euXCn33HOP4/1NRHt6bNCmjnii3mYu2tP9X/Zy2j7nZuKoMKXPC6EIEnM7m2ssGorddoy4DTLTDkFdRjBRypQp42p/HTTnpEP7P//5T+BnFHErZ86cjiuNrCQWW04bzk78fd577z1Xx5g1a5brGax18KtfZ/Ns1qyZ432dDLby4/vnuGuuucbVUqo6iC1RdMWZJ554ImHnDzueRSB/IN50RYOpU6e6OsYzzzwje/bscXWM1q1bR/Q5k9+hfi7bZKRcuXIZrvKVkWXLlkX0uUgCwCKd2dTpYNZs2bJJixYtxC3T8rhp3xeIR73YtPvKzfdVGhisM/k5bS/W2dS/+uorV2lAcJh2fyH4ZfFE0BUqunbtaq/KpUG08fjuOrC1W7durn9jXREhiJYuXSrPPfecVKtWTa699lr5+++/PT/H888/LwULFhSTrF69OsO/lyhRQnLlyiWm8mt/J+3rZqFsFm70K/+baeN8NAjpwgsvdHWMCRMm2EEhbjzyyCO+nxhGy99OOPleycnJdpAYgi3ez1g/2LRpk9x6662OJ/DRiYP++OMPufzyyx2nYeTIkTJ06FDH+5uI9vTYtPfRpo54ot5mJtrT/V32WrdunezevdvRvo0aNZJYW+fz9HklFEFi2kDuppFcl/8+dOiQ5w3XbsydO9fV/g8++GBClxDWmRzd+PPPP6OeMVBnFqKi819NmjSJ6/KJiIw2Brils3M6/Z00eFQb09zOKHzLLbdE9XyNZ4OuLqHuVO7cuUPx/jmuQ4cOrvbXZ+qWLVsknn799Vd7AL/O0j5lypS4ntskJj6LEDnyB2Ll7rvvdhzkNW3aNHnrrbdcr9Qc6SpPJr9D/Vy2ifUKW5mJJP9ow5vOjhfLep6TMqvpedy07wv/CWO92LT7qn379q6fv5MmTZKbb7456tmzdbCZF2V0BIdp9xfCURZPFG1jGjhwoNStW9cuK7/66qt2567XDh8+bLdl6TPZjcaNG9sDXv1Iyw86eaUOapw9e7aMHTtW+vfvb7e/VahQwe7ze+qpp+wAvVi46KKL5M477xTTZFZGdDtQPwz82N9J+6lZKJvFVxjrz0Er75k4zkfr/G7pZAJOV/bVSWFGjx4tfnfOOedI/fr143IurV9SDvJe2J+xiaZtflp/ymil4IxoXVEn/M6bN6+9QqGbVQ41qFMnEgqqMOZVE8uUtKkjnky8x+D/+lUY32fxapvTdvRYm+fz9HnFn70RDripIGplXZfbdbv614l0tjs3g8N0pn1dBtiJ999/Xz744ANJJO2Uc0tnJezdu7c9225G1q9fL23btpWXXnrJ9TnDItJVEk6mHYCZzVwI57TRTAt2bmj0cps2baKu0OugbL1P3M7wqQOsb7rppqhmqalUqZLdiT59+nSJNTeF5qJFi4bi/XNcvXr1XM18tn37dvtZov/GUmpqqnzyySf2Mqznn3++68EWyJyJzyJEjvyBWNGZ3a+44gp7cF00Fi5cKJdddpmrBg114403SkpKSkSfNf0d6teyTSKDxHQV3dq1a2f6OW2EbNiwoe+/o2l53LTvC/8JY73YtPtKZyPUAC+3vvjiC3vVyUWLFmX6WS379OnTRy699NKEvFeROKbdXwhHWdwPZsyYId27d7dXGdZO2qefflp++eWXqOugJw/y++yzz+wy/scff+w6jW5XqXBrzZo19moZp9p01eJ8+fJJqVKl7O/brl07e0WLESNG2PvFkp5z+PDhdjpMk9lstaatrBaU/k7aT81C2Sy+wlh/Dlp5z8RxPlrvLlSokOtVV7X8FO0gU82DQervdLqaWLQ6d+4cl/OYxoRnbCK98MIL8vPPPzveX+tfLVq0+N/3dxM8e+DAAbnhhhvstpsgCmNeNbFMSZs64snEewz+r1+F8X0WjcmTJzvaT9tD9R6Jtck+T59XQhMk5nZGG52NoUaNGvLoo4/anT66fO/8+fPtwc8ZbadbBSNLliz2MsBOaYNJly5dol7G780335S77rpLEu14xcUNvbY6GEI7pF5//XV7AIXOZKibNrLojDraYKK//ffff+9JusNCCy2aB534/fffPU8P/lmxd2vz5s32fdGvX7+IBkx//fXX9qBWXYXDLe1oz549e1T7aEHqo48+kqZNm9qF8gEDBsSkc04bOpwscX1ctWrVQvH+OdFjjz3mKm2aDl01Y9asWeI1nUlOZ1XTQQA62E7/f8SPic8iRI78gVj57bff7OdGJM8Bfc+9++67cvbZZ8vOnTtdnVcHmulKZtEw+R3q57JNRrQhNVaDCrV+G+mxdfB/EALhTMvjpn1f+E8Y68Wm3Vc6k6TTtraTOx10YPGVV15pBxxoQLyWdbRzcO3atfaKY1oer1Klij2ozm2gPILJtPsLwS+L+83MmTPl2WeflVatWkmBAgXsTtvbb79dBg0aZLdP/fXXX7Jx40Z7MiN9zmo/nP5vHaisz2mdiFEHpmo+v/766yMK7o3Etdde68lxwkTb90aNGhXIQaBeOHjwYIZ/96LsEXR+7e+k/dQslM3iK4z15yCV90wc56PB8lpW9GJQ5plnnmn/JpGMB9NVW3Uwc5BWA9bfzW1AXWb0+DrhIGIj7M/YRNH7X9vxnGrQoIH93DzRJZdcIvfdd5/jY86dO1cefPBBCaow5lUTy5S0qSOeTLzH4P/6VRjfZ7Ful7vooovi0ib6u8/T5xkrJJ566im96+K+HTp06LRp6tChg+vjX3755db27dsz/f7r16+3brnlFs+/nxvly5dPyG/ixaZpD7rmzZs7+u633357zNPmNm8E/fe5+OKLPcurBQsWtDp27GgNGzbMmjBhgjV37lxr0qRJ1meffWY98sgjVqVKlTy9LzJ65p3KzTfffNrjNWzY0Hr00UftdO/fv9/VNf3zzz+tBg0auPp+v/76a2jePye66qqrXJ8rS5Ys1n333WctWrTIcmrPnj3Wd999Z3Xv3j2iZ8B5553n+Fy9evVy9X3jLVHpNelZlOhrHUQm5o/jyCfeXo9TbcnJydYFF1xgvfvuu3Z+2Lp1q5WammqtW7fOmjZtmtWnTx+rZs2anp3vyiuvdJQXTHyHBqFsk5EzzjgjJml7+eWXI07D2LFjY5KG3LlzW0eOHLG8ZFoeN+37+uWd9ssvv7hKw9ChQ62gC3O92LT7StvM3H7fRG+rVq1yfJ21TJ+oZ0qinyVuzq3XzQnT7i/FeyvYZfFY2rVrV8Kem15t55xzjuvrEOQ+t1NtKSkp1ldffWWZ7L333svwGjVp0iTRSfQFv/Z3mth+avK72sSyWSKEuf4cpPJekMscTseRbNy40cqePbtn/R+tW7e2hgwZYs2bN88e73X48GFrzZo11uTJk63HH3/c0+e6V3X+SD388MMx/Q27du1qxYObfB60Z6sJz9hEllF27txplStXzvG5c+TIYS1cuPCUxz548KBVq1YtV9/t66+/toImzHnVxDKlyW3qtKfHtz3dxHvM5Dp6EOpXYX6fZebAgQNW1qxZHaXlww8/9DQtQUyfl1IkJDSK128uvvhie0ZYN7755ht75tiOHTvas0RoNKnOnKKzG+oKHjrzg37miy++yHTGuXhr3769vPzyy4lOhrE0vzhZQlJXeEBs6YylOhOMF7NC6bKnGm2uW6wNHDhQcuTI4dnxdMZW3V588UU7urpmzZr2jGIamV61alV7OdhixYpJ4cKF7fPqrKI6q5Y+67Zu3SqrVq2SGTNmyLhx41wtl6ry5csnzZo1C8375+T8pssT6+xsTul115UqddMVXVq2bGnPwFurVi17Nt78+fPbs6xpntaZCTZt2mTPvLt8+XKZN2+e/a7STY8D/+BZBPIHEiU9PV0mTpxob7GmZQyns/eZ+g71e9kms5W25syZk9BrorPtJicn2/nc6zRkzZrV02OalsdN+74IhqDXi027r/r27Stjxoyx22KAWDPt/kLwy+KI/apDYaLlnqFDhxq/SkTevHkzvE4LFiywn9E5c+YUk/m1v5P2dbNQNku8oNefg1TeM3GcT8mSJaVLly72ve6Wtgv/9NNP9hZG9957r50/YlVP1BV9EX9hecYmgq5EuHbtWsf766qCer1PResBI0aMkCZNmtgrkThx22232W07+huGQdDzqollStrUEU8m3mOmC0L9Kozvs8xMmzbNjnGJVlJSkrRp00ZibZrP0+elUAWJ6UN49+7d4he6BLY28Lt56Sj9Tq+++qq9BYkGtpnWeOQnl112mTz55JNR76cFlo0bN9rLmyJ2y5zq/XzXXXcF5hLffffdctVVV8Xs+FqI0Q5P3RJBl/J1OujWj++fE5UrV04++OADufbaaz0rJOmG4ONZBPIHTHDPPfdI/fr1He1r6jvU72WbzILEvK6Dap1eJ3iIlDYMa56bPXu259/Na6blcdO+L4IniPVi0+6rokWL2hPodOrUKdFJgQFMu78Q/LI4Mv5d27ZtyyU6oY716aefyqWXXmr8NSlbtmyG10AHG2mA4WuvvWb0tfJrfyft62ahbOYvQaw/B6m8Z+o4H51s7pNPPrEHXeL0ypcvL+3atZOvvvrK88uk7fBnnHEGlz/BgvyMjTcNIPjyyy8d79+6dWu5//77M/yM3hPPPfecPPzww47OsXPnTvua/vzzz/Yg9DAJYl41sUxJmzriycR7zHRBqF+F8X0Wq4mbNCCzRIkSEmu/+Tx9XkqWkNDo3Ouuu078JHfu3PagxERKZAG/bt26doUmUTTC1WQ6MLFOnTqO9h07dqzn6cE/3XnnnYEZVKQvNx0EFVZayHnggQdC9f451YxvThuNEG48i0D+QJhVqFBBnn/+eVfHMPEdGoSyTTxX29JZk6KtV8dixqpYBImZmMdN+75APOrFpt1XOlju1ltvTci5CxYsKDfddFNCzo3EMO3+QrDL4jg1neX13Xff5fKcEBQ1efJkAsT+j/bh6UrUGXn99dfloosukh9//FH2799vZF7yc38n7etmoWwGU/qVTR3no5N/acAHMvef//wnJpeJVcTg9hkbT7pazIMPPuh4/0KFCsmHH35or0iRmZ49e8r555/v+Fy///67HWgG79CeHh3a1BFP1NvMEoT6lYllr2+//dZxwFo8fOvz9HkpNEFixwvFfpv14NFHH5UiRYok5NyNGzf2LCraqRdeeCHTDo5YuOOOO2K66lFQdOjQwdF+sZj1B/82ePBge8VBP9OlTH/44Qd7GfOw6tGjh71Ma9jePyfr16+fdOnSJdHJgA/xLAL5A0HsLMxMSkqKPeunduy6ZeI7NAhlm9NN1NKkSRNPj+kk4MvrILHChQs7XhEvEqblcdO+LxCPerFp99Xbb78tTZs2jXvZ5vPPP3fdfoHgMe3+QnDL4ji19957T2rUqMHlEbH7K//880+pV68e1+P/aJtFw4YNM70eP/30k1x88cX2zMhlypSxA6Z0cr/jmwlB5H7u76R93SyUzWBKv7Kp43x0UPFdd92VkHNrwEhQBh1qsIrTAO6MJlcIyveHv5+x8aAr/l5//fVy+PBhV+2Lka54q8/jYcOG2RNIOfXss8/awWLwBu3p0aNNHfFEvc0sQahfmVT2WrNmjcyZM8dRP+iNN94osbbG5+nzWqiCxKpVq5bpMryJqMhrISfeSpYsKWPGjLEr0omknRPxXk3t8ssvl3feeSeu5/QrbURx0niny0zv27cvJmnCP18co0aNshsb/UgHok6YMCFhga7xoIO6tDEkjO+fU9HZz7RgDJyIZxEyQv6AW6+88kpCZgjXd97ZZ5/t6fFMeocGpWwTjxW3nAaJRTL7YzSd7l4e71RMy+OmfV8gHvVik+6rXLly2atS1KpVK24z+Y0cOTJmq0rC/0y6vxDssjj+qXfv3glbfdJPSpQoYfdXfvbZZ1K0aNFEJyfQwU/Hjh2TDRs2yN9//20H3B3fEjGIP9783N9J+6l5KJuZy6R+ZZPH+bz66qvSokWLuJ5T3yVffPGFVKlSRYLC6zyswYFuAmAQfF49Y+OV/xcvXuyqDhDtqic6WYSbZ6TWJbRMvXPnTsfHwH/Rnu4MbeqIN+pt5ghC/cqkspfTCZsuuugiKVasmMTaVz5Pn9dC12rct29fu8HCTzQARFcUi5fixYvLxIkTpXTp0uIHL7/8sjRo0CAu57rhhhvsxhMig/9L84CTJadTU1Nl3Lhxnv8++DcN5NTO0cceeyzmAz+j0bZtW5k8eXLEM9cEkQbB6aAuHWwV1vfPyTSPDRgwQIYOHZrwIGL4C88ikD8QK1ou11Uv4jmoWQfieT3bp4nv0CCUbU7Fy7yWI0cOadSoUdT76SQLuiKvV+Jx/5iWx037vkA86sWm3Ve6yqPOvhvrFcW081zbOo9PMJSenu564BmCx7T7C8Eti+O/NJBFJ0zp1auX0ZdEJ9HUgQZLlixJ6IogfnfnnXfaAz7diFcfbCL5vb+T9nWzUDYzk4n9yqaO89E24W+++cbzlbJOR/PUp59+6ug9l0i33HKLvcqpVzp37uzZsRA8Xj9jY+mTTz6RDz/80PH+5cqVk9dff93RvhpY5nSFXbV+/Xq57bbbHO8P2tPdok0d8US9zSxBqF+ZUvb6+uuvHe3npowTpvR5LXRBYjlz5pTvv/9emjRpIn57CHXv3j3m56lQoYL8+uuvng5I86IRRX+TWC8JrUsfjhgxIhCVxnhy2pjy5Zdfep4WnL5Q+sILL8iPP/4oZcuWTehl0sFHr732mnz77beSJ08eCat27drZz0qtgIb9/XMqnTp1krlz58Z9FrRo+KETwDQ8i0D+QKxnBtOZQGP9HOvfv39MB+KZ9A4NUtnmRDpYP3fu3J4cS7+704HYTlYgO514BlmalMdN/L5ArOvFpt1Xeu10dYrbb79dYqFy5coybdq0f5Shdu/e7bpchuAy6f4yXVDL4rGiz64uXboEYhUqDWSZMGGCPPDAA2Iq7afUPtHVq1fLk08+Kfny5Ut0knx/v+tA02zZsjk+hglBYkHo76R93TyUzcxhar+yyeN8dEWr3377LeYTw2g+0En2rrnmGgkabYP3KrBLg2bivXr64cOHHe8bhHpJkMSqjTIWli9f7mqVRZ1QZNiwYZI/f37Hx3jjjTfsOpdTGgSrx0D0aE/3Bm3qiDfqbWYIQv3KhLLXjh07ZNKkSY7qX1dccYXE2g6fpy8WQhckdrxCphV2XZnHTaO61wYOHGjPBhGrNF188cXy559/So0aNcRvSpQoYd9czZo18/zYOjuNziqkMxlphQr/dO211zpaDUojZvfu3cvljKPWrVvLggUL7GdXvAftaOeVzjozb9486dq1q69WNfOSFm4GDx5s528vZ7by+/vnVKpXr27Peq6zHOnAMz/QxrCbbrrJfqZroCISg2cRyB+IVYeyLtv9zDPPxKTMrpVyfX889NBDEmsmvUODVLY5TgcTnHPOOZ4cy02g13nnnedJGnQSiVgPxDA5j5v4fYFY14tNu6+042nIkCH24OOKFSt6ckxd7UsHyc2ePVvq1av3j7/t2rXL1bG9CqRG4ph0f5kuiGXxWNHv/9Zbb8nGjRvtFYF05aWSJUuK3+q8Dz/8sPz999+BWwXCC8WKFZN7771XJk+eLCtXrpRHH31U8ubNm+hkBYbWYb/77jvHgzPOOOMMMUFQ+jtpXzcLZbNwo1/Z7HE+uipqPCaGCepgQ3Xfffd58tvp4O145gEN9NmyZYvjdqAXX3zR8zSZKB5tlF46cuSIverhvn37HB+jZ8+ervuOdBKO4cOHu5qk58EHH7QnIUJkaE/3vr2PNnXEG/U2M9Cenvj32ciRIyUtLS3q/e666y773RBrI32evpiwQm7dunXWQw89ZJUpU8bSr+v1dujQoajTNH/+fKtFixaepaFkyZLWRx99ZKWnp//rXB07dnR1bK+lpqZaffr0sbJnz+76eyclJdnfb8uWLac8l5vvXr58eStMnn/+eUfXYfDgwTFJj15fN7992H6fU9m0aZP12GOPWcWLF4/Js+v4liNHDqtDhw7W7NmzY/I9Nm/ebI0aNcq6//77rXr16lnJyckx/T6n2/Qd0LdvX2vPnj2Wye+f0zl69Kj9HmnevHncf5tKlSpZd95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" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1732 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "pc = az.plot_dist(\n", + " idata_seg,\n", + " var_names=[\"tau\"],\n", + " visuals={\n", + " \"title\": {\"text\": r\"Posterior of between-segment SD $\\tau$ (one study, six segments)\"}\n", + " },\n", + ")\n", + "az.add_lines(\n", + " pc,\n", + " values=np.sqrt(tau2_DL),\n", + " visuals={\"ref_line\": {\"color\": \"C1\", \"label\": f\"DerSimonian–Laird τ = {np.sqrt(tau2_DL):.2f}\"}},\n", + ")\n", + "pc.get_viz(\"plot\").legend();" + ] + }, + { + "cell_type": "markdown", + "id": "2e5f189d", + "metadata": {}, + "source": [ + "Three estimators, three commitments about how much the segments share. The fixed-effect ANOVA assumes one common effect and pools completely; the random-effects ANOVA admits between-segment variance and estimates it by moments; the hierarchical model carries that variance as a posterior. The grouping factor was the segment. Replace it with \"study\" and the model is untouched: meta-analysis is the random-effects analysis of variance with studies as the groups, and the index $k$ ranges over experiments rather than segments. The rest of this notebook makes exactly that substitution. Making that substitution is mechanical. What it reveals is substantive: once studies replace segments, τ becomes the quantity the replication programme was designed to estimate.\n", + "\n", + "## The hierarchical re-framing\n", + "\n", + "The model is the one we just fit, with markets in place of segments. Let $\\theta_k$ be the true treatment effect in market $k$, and let $\\hat d_k$ be the observed estimate from market $k$'s experiment with standard error $s_k$. The single-experiment view treats each $\\hat d_k$ as the answer to its own question; vote-counting and pool-everything are degenerate cases of that view. The hierarchical view writes:\n", + "\n", + "$$\n", + "\\theta_k \\sim \\mathcal{N}(\\mu, \\tau), \\qquad \\hat d_k \\mid \\theta_k \\sim \\mathcal{N}(\\theta_k, s_k),\n", + "$$\n", + "\n", + "where $\\mu$ is the population mean effect across markets and $\\tau$ is the between-market standard deviation. $\\mu$ tells the team what to expect on average; $\\tau$ tells them how variable that expectation is across markets. Neither quantity is recoverable from any single experiment. Both are recoverable from the joint." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b2a086f6", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:32.156776Z", + "iopub.status.busy": "2026-06-01T17:59:32.156571Z", + "iopub.status.idle": "2026-06-01T17:59:32.165025Z", + "shell.execute_reply": "2026-06-01T17:59:32.164553Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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marketN_per_armtrue_thetad_hatsez_score
0Market A2000.2200.4830.4231.143
1Market B2501.0020.9980.3592.782
2Market C3001.0981.3830.3304.189
3Market D3500.5590.4930.2961.663
4Market E4000.6070.4380.2771.581
5Market F5000.1550.1010.2550.395
6Market G700-0.0570.0720.2120.338
7Market H1200-0.050-0.0010.163-0.004
\n", + "
" + ], + "text/plain": [ + " market N_per_arm true_theta d_hat se z_score\n", + "0 Market A 200 0.220 0.483 0.423 1.143\n", + "1 Market B 250 1.002 0.998 0.359 2.782\n", + "2 Market C 300 1.098 1.383 0.330 4.189\n", + "3 Market D 350 0.559 0.493 0.296 1.663\n", + "4 Market E 400 0.607 0.438 0.277 1.581\n", + "5 Market F 500 0.155 0.101 0.255 0.395\n", + "6 Market G 700 -0.057 0.072 0.212 0.338\n", + "7 Market H 1200 -0.050 -0.001 0.163 -0.004" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "K = 8\n", + "TRUE_MU = 0.4\n", + "TRUE_TAU = 0.5\n", + "SIGMA_OBS = 4.0\n", + "MARKET_NAMES = [f\"Market {chr(65 + i)}\" for i in range(K)]\n", + "# Per-market sample sizes vary; smaller markets have noisier estimates, which\n", + "# is the regime where partial pooling does substantively visible work.\n", + "N_PER_MARKET = np.array([200, 250, 300, 350, 400, 500, 700, 1200])\n", + "meta_rng = np.random.default_rng(20)\n", + "\n", + "\n", + "def simulate_meta_dataset_gaussian(K, N_per_market, true_mu, true_tau, sigma_obs, rng):\n", + " theta = rng.normal(true_mu, true_tau, size=K)\n", + " d_hat = np.zeros(K)\n", + " s = np.zeros(K)\n", + " for k in range(K):\n", + " N_k = int(N_per_market[k])\n", + " y_A = rng.normal(10.0, sigma_obs, size=N_k)\n", + " y_B = rng.normal(10.0 + theta[k], sigma_obs, size=N_k)\n", + " d_hat[k] = y_B.mean() - y_A.mean()\n", + " s[k] = np.sqrt(y_A.var(ddof=1) / N_k + y_B.var(ddof=1) / N_k)\n", + " return theta, d_hat, s\n", + "\n", + "\n", + "true_theta, d_hat_obs, se_obs = simulate_meta_dataset_gaussian(\n", + " K, N_PER_MARKET, TRUE_MU, TRUE_TAU, SIGMA_OBS, meta_rng\n", + ")\n", + "markets_df = pd.DataFrame(\n", + " {\n", + " \"market\": MARKET_NAMES,\n", + " \"N_per_arm\": N_PER_MARKET,\n", + " \"true_theta\": true_theta,\n", + " \"d_hat\": d_hat_obs,\n", + " \"se\": se_obs,\n", + " \"z_score\": d_hat_obs / se_obs,\n", + " }\n", + ")\n", + "markets_df.round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "958dfc38", + "metadata": {}, + "source": [ + "The per-market `z_score` column is what a frequentist replication exercise would consult: anything above 1.96 in absolute value counts as \"significant\", anything below does not. The columns disagree about how many markets \"worked\"; the underlying true effects disagree less. This is the gap the hierarchical model closes. The quantity no single experiment can recover is τ.\n", + "\n", + "## No pooling, complete pooling, partial pooling\n", + "\n", + "Three estimators reflect three commitments about how much the markets share. *No pooling* fits each market in isolation; the per-market estimate is $\\hat d_k$. *Complete pooling* fits a single mean across all markets, treating them as draws from one distribution with no between-market variance. *Partial pooling* fits the hierarchical model above and lets the data weigh how exchangeable the markets are. The PyMC code below makes all three explicit so the shrinkage that distinguishes them becomes visible." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "ea8e78de", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:32.166252Z", + "iopub.status.busy": "2026-06-01T17:59:32.166169Z", + "iopub.status.idle": "2026-06-01T17:59:33.447380Z", + "shell.execute_reply": "2026-06-01T17:59:33.446901Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "NUTS[nutpie]: [mu]\n", + "NUTS[nutpie]: [mu, tau, theta_offset]\n" + ] + } + ], + "source": [ + "coords = {\"market\": MARKET_NAMES}\n", + "\n", + "with pm.Model(coords=coords) as complete_model:\n", + " mu_complete = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n", + " pm.Normal(\"d_hat\", mu=mu_complete, sigma=se_obs, observed=d_hat_obs, dims=\"market\")\n", + "\n", + "with complete_model:\n", + " idata_complete = pm.sample(\n", + " draws=1000,\n", + " tune=1000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )\n", + "\n", + "with pm.Model(coords=coords) as partial_model:\n", + " mu = pm.Normal(\"mu\", mu=0.0, sigma=1.0)\n", + " tau = pm.HalfNormal(\"tau\", sigma=1.0)\n", + " theta_offset = pm.Normal(\"theta_offset\", mu=0.0, sigma=1.0, dims=\"market\")\n", + " theta = pm.Deterministic(\"theta\", mu + tau * theta_offset, dims=\"market\")\n", + " pm.Normal(\"d_hat\", mu=theta, sigma=se_obs, observed=d_hat_obs, dims=\"market\")\n", + "\n", + "with partial_model:\n", + " idata_partial = pm.sample(\n", + " draws=2000,\n", + " tune=2000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "35d9a55e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:33.448789Z", + "iopub.status.busy": "2026-06-01T17:59:33.448713Z", + 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 1066, + "width": 3967 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "no_pool_mean = d_hat_obs\n", + "no_pool_se = se_obs\n", + "complete_pool_mean = idata_complete.posterior[\"mu\"].mean().item()\n", + "complete_pool_se = idata_complete.posterior[\"mu\"].std().item()\n", + "partial_pool_summary = az.summary(idata_partial, var_names=[\"theta\"], kind=\"stats\")\n", + "partial_pool_mean = partial_pool_summary[\"mean\"].values.astype(float)\n", + "partial_pool_sd = partial_pool_summary[\"sd\"].values.astype(float)\n", + "\n", + "forest = pd.DataFrame(\n", + " {\n", + " \"market\": MARKET_NAMES,\n", + " \"no_pool_mean\": no_pool_mean,\n", + " \"no_pool_lo\": no_pool_mean - 1.96 * no_pool_se,\n", + " \"no_pool_hi\": no_pool_mean + 1.96 * no_pool_se,\n", + " \"partial_mean\": partial_pool_mean,\n", + " \"partial_lo\": partial_pool_mean - 1.96 * partial_pool_sd,\n", + " \"partial_hi\": partial_pool_mean + 1.96 * partial_pool_sd,\n", + " }\n", + ").round(3)\n", + "\n", + "fig, ax = plt.subplots(figsize=(20, 5.5))\n", + "y_pos = np.arange(K)\n", + "ax.errorbar(\n", + " forest[\"no_pool_mean\"],\n", + " y_pos - 0.18,\n", + " xerr=[\n", + " forest[\"no_pool_mean\"] - forest[\"no_pool_lo\"],\n", + " forest[\"no_pool_hi\"] - forest[\"no_pool_mean\"],\n", + " ],\n", + " fmt=\"o\",\n", + " color=\"C0\",\n", + " label=\"No pooling\",\n", + " capsize=3,\n", + ")\n", + "ax.errorbar(\n", + " forest[\"partial_mean\"],\n", + " y_pos + 0.18,\n", + " xerr=[\n", + " forest[\"partial_mean\"] - forest[\"partial_lo\"],\n", + " forest[\"partial_hi\"] - forest[\"partial_mean\"],\n", + " ],\n", + " fmt=\"s\",\n", + " color=\"C3\",\n", + " label=\"Partial pooling\",\n", + " capsize=3,\n", + ")\n", + "ax.axvline(\n", + " complete_pool_mean,\n", + " color=\"black\",\n", + " linestyle=\"--\",\n", + " alpha=0.7,\n", + " label=f\"Complete pooling (mean = {complete_pool_mean:.3f})\",\n", + ")\n", + "ax.axvline(0.0, color=\"grey\", linestyle=\":\", alpha=0.5)\n", + "ax.set_yticks(y_pos)\n", + "ax.set_yticklabels(MARKET_NAMES)\n", + "ax.set_xlabel(\"Estimated treatment effect\")\n", + "ax.set_title(\"Forest plot: three pooling strategies on eight markets\")\n", + "ax.legend(loc=\"upper right\", bbox_to_anchor=(1.0, 1.0), framealpha=0.95)\n", + "plt.tight_layout();" + ] + }, + { + "cell_type": "markdown", + "id": "33737f97", + "metadata": {}, + "source": [ + "The partial-pooling estimates are pulled toward the population mean: the canonical *shrinkage* picture {cite:p}`gelman2006multilevel`, {cite:p}`gelman2020regression`. The pull is strongest for the markets whose individual estimates are noisiest (widest no-pooling intervals) or most extreme; it is weakest for markets whose estimates are tight and central. This is the data-driven version of \"borrowing strength\" that vote-counting cannot do and complete-pooling does only by force." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "261a8315", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:33.647890Z", + "iopub.status.busy": "2026-06-01T17:59:33.647802Z", + "iopub.status.idle": "2026-06-01T17:59:33.932721Z", + "shell.execute_reply": "2026-06-01T17:59:33.932284Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 1023, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(20, 5))\n", + "for k in range(K):\n", + " ax.plot([0, 1], [no_pool_mean[k], partial_pool_mean[k]], color=\"grey\", alpha=0.5, zorder=1)\n", + " ax.scatter(0, no_pool_mean[k], color=\"C0\", zorder=3, s=55)\n", + " ax.scatter(1, partial_pool_mean[k], color=\"C3\", zorder=3, s=55)\n", + " ax.text(1.04, partial_pool_mean[k], MARKET_NAMES[k], ha=\"left\", va=\"center\", fontsize=9)\n", + "ax.axhline(\n", + " complete_pool_mean,\n", + " color=\"black\",\n", + " linestyle=\"--\",\n", + " alpha=0.7,\n", + " label=f\"Complete-pooling mean = {complete_pool_mean:.3f}\",\n", + ")\n", + "ax.set_xticks([0, 1])\n", + "ax.set_xticklabels([\"No pooling\", \"Partial pooling\"])\n", + "ax.set_xlim(-0.15, 1.25)\n", + "ax.set_ylabel(\"Estimated treatment effect\")\n", + "ax.set_title(\"Shrinkage: per-market estimates pulled toward the population mean\")\n", + "ax.legend(loc=\"lower right\");" + ] + }, + { + "cell_type": "markdown", + "id": "30196761", + "metadata": {}, + "source": [ + "### The substance lives in $\\tau$\n", + "\n", + "The hierarchical model returns two population-level quantities, and the conventional reporting habit of leading with $\\mu$ obscures the more important one. The posterior of $\\tau$, the between-market standard deviation of true effects, is what tells the team how transportable any single result is to a new context. A small $\\tau$ means the markets are nearly exchangeable, and the experiment generalises cleanly; a large $\\tau$ means the markets are heterogeneous, and the next market is a meaningfully new experiment. Reporting only $\\mu$ collapses this into a point and hides the variability that the next stakeholder will live with." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "74a6c277", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:33.934141Z", + "iopub.status.busy": "2026-06-01T17:59:33.934048Z", + "iopub.status.idle": "2026-06-01T17:59:34.138886Z", + "shell.execute_reply": "2026-06-01T17:59:34.138478Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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XxPkNNZnNBABT7fp1zXFF6+LU3L6T/fEXD+/yQAAAAAAAgNOmOAbAjDGaz8entx5Mzb1hQ2sm8wBAVnK5XPzB09dGU2VZava2PZ3x7X2HM5kLAAAAAACYuxTHAJgxfnjoWOw+0ZeYWVZdEc8tYCMLAMw2NWUl8d6L1xf0Q9oHH94VnX2DGUwFAAAAAADMVYpjAMwYhW0ba4niXC6TeQAgaxc21MRbNi5LzXUPDsefPLAj8vl8JnMBAAAAAABzj+IYADPCpiMn48HD3YmZRWUlcc3KxsxmAoDp8AtnLovz6hem5u5pPxb/trsjk5kAAAAAAIC5R3EMgBnhUwVsG3vt2uaoKC7OZB4AmC4lRbl430XrY2Fp+nveXz+yOw6c7M9kLgAAAAAAYG5RHANg2o194P3dA12JmfKiXLxmbXNmMwHAdGqpLo/fu3BNaq5vZDTe98D2GHFlJQAAAAAAMEElE30BAEy2m7a3xWhK5qWrlkRdeanDB/hZyuui+MxfST6b8jpnN8u8YHlD3HnwSHxnf3K5+uHDJ+LmbW3xhg2tmc0GAAAAAADMfrl83q+mAzB9jg8Mxcu//mD0jzx1dSwXEbe+6IJYvqAy09kAYCa8T77+O4/E4f6hxFx5cVF8+qrzvFcCAAAAAAAFc1UlANPq8zvbE0tjYy5vXeyDcADmpdry0viDp69NzQ2MjMb7H9wZfi8IAAAAAAAolOIYANNm7EPuW3YcSs290dVbAMxjz2qui1etbkrNPdjZHV/a1ZHJTAAAAAAAwOynOAbAtPn63s44OpB89db59Qvj3PqFmc0EADPRb563MpZWl6fmPvzYnmjvHchkJgAAAAAAYHZTHANgWoxdpXXTtrbU3BtsGwOAqCopjj8s4MrKnuGR+OBDu1xZCQAAAAAApFIcA2Ba3Nt+PHaf6EvMrFhQEZe11GU2EwDMZE9rrI1XF3Bl5d2Hjsa39ndlMhMAAAAAADB7KY4BMC1u2n4wNfP69a1RlMtlMg8AzAZvO3dFLKksS8391SO7o3twOJOZAAAAAACA2UlxDIDM7ezujR+1H0/MLCoriatXNmQ2EwDMBgtKS+L3LlyTmjs6MBR/9/jeTGYCAAAAAABmJ8UxADJ387a21Myr1zRFRXFxJvMAwGzynJa6eNHy9HL1F3e1x+NHTmQyEwAAAAAAMPsojgGQqWMDQ/GNvZ2JmZJcLq5d25zZTAAw27zz/FXj2zmT5CPiAw/ujOHRsf8EAAAAAADwXymOAZCpse0nAykfYL9weUPUV5RlNhMAzDaLykvHy2Npth7vjVt3HMpkJgAAAAAAYHZRHAMgM0Ojo/G5Aj68vmF9SybzAMBsNla0vqixNjX3D5v2RnvvQCYzAQAAAAAAs0fy3SYAMIm+va8rDvcPJWae1lgTGxZVO3eACcgP90b+2KbETG7RWZErqXKuc0gul4vfvXB1vP47j8RQwjbP3uHR+OtHd8efXnJGpvMBAAAAAAAzm+IYAJnI5/Nx8/a21NwN62wbA5iwgaMx8uRHEyMlF94YoTg256xYWBk/d8bS+Pjm/Ym5Ow4ciR93HI+LlqRvKAMAAAAAAOYHV1UCkImHDnfHlmM9iZll1eXxnJY6TwQAJuDNZywdfw9N85eP7Irh0VFnCwAAAAAAjFMcAyAThWwbe926lijK5TKZBwDmivLiovidC9ek5nZ298Xnd7ZnMhMAAAAAADDzKY4BMOX2n+yP7x88mphZUFocL121xNMAgFNwSdOiuGpZfWruHzbti6MDQ84YAAAAAABQHANg6n12e1vkUzKvWLUkqkqKPQ4AOEX/47yVUVmc/LtBJ4dG4u+f2OuMAQAAAAAAxTEAptbJoeH46p6OxExxLuK6dS0eBQCchiWV5fHzZy5Lzf3bro548uhJZw0AAAAAAPOcqyoBmFJjH073Do8mZp63tD6aq8o9CQA4TTesb4ll1cnvqWNbQP/PI7sjn0/bBwoAAAAAAMxlimMATJnh0XzcuuNQau5628YAYFKUFxfFO85blZp7tOtE3H6gy6kDAAAAAMA8pjgGwJT53sEj0dY7kJg5e/GCOLd+oacAAJPkOS11cWnTotTcRx7bG4MjyVtBAQAAAACAuUtxDIApc/P2ttTMDbaNAcCkyuVy41vHinO5xNzB3oGCNoMCAAAAAABzk+IYAFNiy7Ge8WuwkjRVlsXzltZ7AgAwyVbVVMbr1jWn5v75yf1xfGDI+QMAAAAAwDykOAbAlPhcARtMXru2OUqKkrehAACn5i1nLovaspLEzImhkfj4k/sdMQAAAAAAzEOKYwBMuuODQ/HNvZ2JmYrionjF6ianDwBTZGFZSfzSxmWpuc/taI+9J/o8BwAAAAAAmGcUxwCYdF/Z3RkDo/nEzNUrGqMmZQsKAHB6XrWmKVYsqEjMjOTz8ZHH9zpqAAAAAACYZxTHAJhUYx8+f76AayqvXWvbGABMtZKionj7uStTc3cePBKPHO72QAAAAAAAYB5RHANgUt1z6Fgc7B1IzDytoSbW1VY7eQDIwHNb6sbfe9OMbR3L55M3hgIAAAAAAHOH4hgAk+rWHW2pmWvXNjt1AMhILpeL3zwvfevYI10n4oeHjmUyEwAAAAAAMP0UxwCYNHtP9MWP2o8nZhory+Ly1jqnDgAZ2li3IF68oiE197dP7I1RW8cAAAAAAGBeUBwDYNJ8bueh1MyrVzdFSZG3HwDI2q+dvSJKi3KJme3He+Pb+w5nNhMAAAAAADB9fHIPwKToHR6Jr+7uTMyU5HLxitVLnDgATIPmqvK4dk36ddEf3bQvhkZHM5kJAAAAAACYPopjAEyKb+ztjJ7hkcTMVcvqo76izIkDwDR585lLo6qkODFzoGcg/m1XR2YzAQAAAAAA00NxDIDTls/n49Yd6ddUXrs2fcsJADB16spL4w0bWlJzH9+8P/pSCuEAAAAAAMDspjgGwGl76HB37OzuS8ycuag6zlm8wGkDwDS7YV1r1JWXJGaODAzFLQWUwgEAAAAAgNlLcQyA01bItrHXrm2OXC7ntAFgmlWXFscvnLksNfeprQfj5NBwJjMBAAAAAADZUxwD4LS09w7E9w4eSczUlpXEVcvrnTQAzBCvWt0ULVXliZnuweG4ZbutYwAAAAAAMFcpjgFwWr64qz1G8smZV6xaEhXFxU4aAGaIsuKi+OWzlqfmPrPtYJwYtHUMAAAAAADmIsUxAE7Z4MhofGlXR+obzavWNDllAJhhXrSiIVYtrEzMnBgaiZu3t2U2EwAAAAAAkB3FMQBO2R0HuuLowFBi5jktddFaXeGUAWCGKc7l4q0bl6XmbtrWFscHk9/vAQAAAACA2UdxDIBTduuOQ6mZ165tdsIAMENduaw+1tQkbx3rGR6Jz2y1dQwAAAAAAOYaxTEATsmWYz3x+JGTiZmVCyrioiW1ThgAZqiiXC5+6azlqbnPbm+LYylbRgEAAAAAgNmlZLoHAGB2+tLO9oK2jeVyuUzmAZjXShdG0fKXpWbgZ7midXGsr62Kbcd7n/KA+kZG49NbD8bbzl3pEAEAAAAAYI7I5fP5/HQPAcDs0js8Ei+57YHxfz6VqpKi+Mo1T48FpTrKADDTff/gkfide7YkZsbe27/04qdFbXlpZnMBAAAAAABTx1WVAEzYt/YdTiyNjXnx8kalMQCYJS5rqYszF1UnZnqHR+Om7W2ZzQQAAAAAAEwtxTEAJuyLBVxT+ao1TU4WAGaJsaulf/ms5am5W7YfihODw5nMBAAAAAAATC3FMQAmZPPRk/HksZ7EzNl1C2JDytYSAGBmeVbzothYl/z+3TM8ErfsOJTZTAAAAAAAwNRRHANgQr60K33b2CtXL3GqADALt4695cxlqbmbtx2MnqHkK6sBAAAAAICZT3EMgIKNfUj8rX2HEzPVJcXxguUNThUAZqHLWupifW1VYqZ7aCQ+t9PWMQAAAAAAmO0UxwAo2Df3HY7e4dHEzItXNERlSbFTBYDZunVsY/rWsc9sPRh9w7aOAQAAAADAbKY4BkBB8vl8gddUNjlRAJjFrmhdHGtqKhMzxwaH44s7078vAAAAAAAAZi7FMQAK8uSxnthyrCcxc/biBbFhUbUTBYBZrCiXi184s4CtY9sOxuBI8iZSAAAAAABg5lIcA6AghWwVeZVtYwAwJ1y5rD5WLqhIzHT2D8U39h3ObCYAAAAAAGByKY4BkOrk0HB8K+WD4QWlxfGCZfVOEwDmgOJcLn6+gK1jn9pyIEbz+UxmAgAAAAAAJpfiGACpvrn3cPSlXEV19YrGqCgpdpoAMEe8cHlDtFaVJ2b2nOyP7x88ktlMAAAAAADA5FEcAyBRPp+PL+5Kv6bylauXOEmAaZIfHYp8z4HkP6NDng8TUlKUi9dvaE3NfXLLwfHvFwAAAAAAgNmlZLoHAGBm23T0ZGw73puYOXfxglhXW53ZTAD8lL6OGH7oxsRjKbnwxojqpY6OCXnZysb4+OZ9cXRg+CkzTxw9GQ8e7o6nN9Y6XQAAAAAAmEVsHAMgUSHbxl61pskpAsAcNHYN9XVrW1Jz/7rlYCbzAAAAAAAAk0dxDICndHJoOL69ryvxhBaWFseVy+qdIgDMUdeubY6qkuQfHe9pPxZbj/VkNhMAAAAAAHD6FMcAeEpf33s4+kdGE0/o6hWNUVFc7BQBYI6qKSuJV65O3y76r1sPZDIPAAAAAAAwORTHAPiZ8vl8fGmnayoBgIjr17VESS6XeBTf2dcVB072Oy4AAAAAAJglFMcA+JkeP3Iytnf3Jp7OefULY01NlRMEgDmuqao8XryiITEztqP009sOZjYTAAAAAABwehTHAPiZvrK7I/VkXlXAtVUAwNzwxg2tqZmv7u6II/1DmcwDAAAAAACcHsUxAP6bvuGR+Pb+rsSTqSktjucvW+z0AGCeWF1TFZe31iVmBkbzccuOtsxmAgAAAAAATp3iGAD/zXcPHIne4ZHEk3nxisaoKC52egAwj7xpw9LUzOd2HIqeoeTvIwAAAAAAgOmnOAbAKV1T+YrVS5wcAMwz59YvjAsbFiZmTgyNxL/tas9sJgAAAAAA4NQojgHwX+w72RcPHu5OPJWNddWxrrbayQHAPPRzZ6RvHfvM9rYYGh3NZB4AAAAAAODUKI4B8F/ctqcz9URettK2MQCYry5tWhTraqsSM519g/GNvYczmwkAAAAAAJg4xTEA/tNIPh9fTSmOlRfl4oXLG5waAMxTuVwufm5Da2ruU1sPxmg+n8lMAAAAAADAxCmOAfCf7ms/Nr4hJMkVS+tjYVmJUwOAeezKZQ3RUlWemNl9oi/uOXQss5kAAAAAAICJURwD4D99ZXcB11Suck0lAMx3JUW5eMP6ltTcTdvaMpkHAAAAAACYOMUxAMYdGxiK7x08kngaY5tFnt5Y48QAgPEy+aKULaQ/7jweW4/1OC0AAAAAAJiBFMcAGPfNfYdjOJ9PPI2XrmyMolzOiQEAUVFSHNeubU49CVvHAAAAAABgZlIcAyDy+Xx8eXdH4kmM1cVestI1lQDA/+81a5qjrCi5VP6tfYejs2/QsQEAAAAAwAyjOAZAbDnWE9uP9yaexEVLaqOlutxpAQD/aXFFaVy9ojHxRMY2mn5uxyGnBgAAAAAAM4ziGADxlZRtY2Netsq2MQDgv7t+fUvqsXxh56HoGx5xfAAAAAAAMIMojgHMcwMjo/HNfYcTMwtLi+Py1sWZzQQAzB5raqri0qZFiZnuoZG4bU9nZjMBAAAAAADpFMcA5rk7Dx6JE0PJG0BetLwhyou9ZQAAP9vrC9g6dtO2thjN5x0hAAAAAADMEFoAAPPcV11TCQCcpouW1Ma6mqrEzP6e/rir7aizBgAAAACAGUJxDGAeO9jTHz/uOJ6YWV9bFWcsqs5sJgBg9snlcnFDQVvHDmYyDwAAAAAAkE5xDGAe+9qezki7MOplq5aMfxgMAJDkhcsbor6iNDHz0OETsfnoSQcJAAAAAAAzgOIYwDw1ms/HV/d0JmZKi3Lx4uUNmc0EAMxeZcVF8dq1zam5z9g6BgAAAAAAM4LiGMA89UBnd7T1DiRmntuyOGrLkzeHAAD8h1etbory4uQfM2/f3xXtKd+DAAAAAAAAU09xDGCe+uqejtTMy1Y1ZjILADA3LCovjZesSP7+YSQfccuOQ5nNBAAAAAAA/GyKYwDzUM/QSNx54EhiprGyLC5uWpTZTADA3HDD+pbUzJd2tY9/PwIAAAAAAEwfxTGAeei7B7qif2Q0MfPSlY1RnMtlNhMAMDesWFgZl7XUJWZODo3EV3anbz8FAAAAAACmTskU/t0AzFBf29uZmrkm5ZopAGaQksrI1T89NQNZbh27q+1oYubm7W1x7drmKClSVAcAAAAAgOmgOAYwz7T1DMQDnd2JmfPqF45vCwFgdsiVL46Sjb863WPAf3paQ02csag6thzrecpTaesdiO+3HYnnL613cgAAAAAAMA1cVQkwz3xjX/q2sattGwMATkMul4vXr29Jzd20rc05AwAAAADANFEcA5hH8vl8fG1PcnGsrCgXVy2z+QMAOD1j3080VpYlZh7tOhGbjpx01AAAAAAAMA0UxwDmkSeOnoy9J/sTM5e1LI6aMjcZAwCnp6SoKK5b25yau2n7QUcNAAAAAADTQHEMYB5J2zY25pqVjZnMAgDMfa9c3RQVxck/dt6+/0i09w5kNhMAAAAAAPD/KI4BzBODI6Px7X2HEzN15SVxSVNtZjMBAHPb2BbTl6SU0kfy+fjcjkOZzQQAAAAAAPw/imMA88QPDh2N7qGRxMyLljeOXysFADBZrl/Xkpr50q726BtO/j4FAAAAAACYXNoBAPOEayoBgOmwYmFlPKe5LjEzVm6/rYArtQEAAAAAgMmjOAYwDxwdGIofHDqWmFlbUxkbaqsymwkAmD9uWJ++dezm7W0xms9nMg8AAAAAAKA4BjAvfHvf4RhJ+SD2mpVLIpfLZTYTADB/PL2xJtalFNT3neyPH6YU3QEAAAAAgMlj4xjAPPC1vZ2pbwYvWt6Q2TwAwPwyVk6/YV0BW8e2tWUyDwAAAAAAoDgGMOft7O6NzUd7EjMXN9VGY2VZZjMBAPPPC5c3xOLy0sTMjzuPx7bjyd+3AAAAAAAAk8PGMYA57ut7kreNjblmRWMmswAA81dZcVG8Zm1Tas7WMQAAAAAAyEZJRv87AEyDkXw+vr7vcGKmqqQ4Lm9dnNlMAEy+fM+BGH7oxsRMyYU3Rq56qeNnWr16dXN84skDMTiaf8rMN/cdjl8/Z0XUV9iGCgAAAAAAU8nGMYA57IGO49HZN5iYuXLZ4qgoKc5sJgBg/lpcURovTtl0OjSajy/sbM9sJgAAAAAAmK8UxwDmsNv2uqYSAJhZrl/Xkpr5/M5DMTAymsk8AAAAAAAwXymOAcxRPUMjceeBI4mZlqryuKChJrOZAADW1lbFxUtqEw/i6MDw+JWVAAAAAADA1FEcA5ij7jzYFf0pmzquXtEQRblcZjMBAIy5YX361rHPbmuLfD7vwAAAAAAAYIoojgHMUbftSb+m8uoVjZnMAgDwky5pWhSrFlYmHsr27t74ccdxBwcAAAAAAFNEcQxgDmrrGYgHOrsTM+cuXhArUj6wBQCYCmMbT1+3rjk1d9P2Ng8AAAAAAACmiOIYwBz0zX3p28auWbkkk1kAAH6Wa1Y0Rk1ZSeLh/PDQsdjd3ecAAQAAAABgCiiOAcwx+Xw+vpZyTWVpUS6uWlaf2UwAAD+toqQ4XrW6KfVgPmvrGAAAAAAATAnFMYA55omjJ2PPyf7EzGUtdakbPgAAptq1a5uiOJdLzNy2tzOODwx5GAAAAAAAMMkUxwDmmLRtY2Ne4ppKAGAGWFJZHi9I2YI6MDIaX9zVkdlMAAAAAAAwXyiOAcwhgyOj8e39XYmZuvKSuKSpNrOZAACSXL++JfWAPrejLYZGRx0kAAAAAABMIsUxgDnkB4eORvfgcGLmhcsboqTIl38AYGbYWLcgLmhYmJjp7B+K21PK8QAAAAAAwMRoDgDMs2sqr1nRmMksAACFumFd+taxm7a1RT6fd6gAAAAAADBJFMcA5ohjA0Pxg0PHEjNrayrjjEXVmc0EAFCIy1oXx9Lq8sTMk8d64uGuEw4UAAAAAAAmieIYwBzx7X2HYyRlC8fVKxojl8tlNhMAQCGKc7m4bm361rHPbD3oQAEAAAAAYJIojgHMEbft7Uz9gv9i11QCADPUy1YtieqS4sTMXW1HY8+JvsxmAgAAAACAuUxxDGAO2NXdG5uP9iRmLm6qjcbKssxmAgCYiOrS4njF6iWJmbHdqp+2dQwAAAAAACaF4hjAHPD1vYdTM9fYNgYAzHBj11UWp9yq/fW9ndHVP5jVSAAAAAAAMGcpjgHMcqP5/PgHqEmqSori8tbFmc0EAHAqWqrL48pl9YmZwdF83LrjkAMGAAAAAIDTpDgGMMs92NkdHX3JWzeev7Q+KkqKM5sJAOBUvXHD0tTM53ccit7hEYcMAAAAAACnQXEMYJb7Wsq2sTHXrGzMZBYAgNN1xqLquKixNjHTPTQSX9nd4bABAAAAAOA0KI4BzGJ9wyNxx/6uxExzVVlc2FCT2UwAAKfrjRtaUzM3bWuL4dG8wwYAAAAAgFOkOAYwi9158Ej0jYwmZq5e0RhFuVxmMwEAnK5nNtXGutqqxExb70DccSC5QA8AAAAAADw1xTGAWezre9KvqRwrjgEAzCa5XC7esD5969inth6MfN7WMQAAAAAAOBWKYwCzVEffQPy443hi5uy6BbFyYWVmMwEATJYXLq+PJZVliZktx3rigc5uhw4AAAAAAKdAcQxglvrm3sORfEllxNUrbRsDAGankqKiuH5dS0FbxwAAAAAAgIlTHAOYhcauZPra3uRrKktyuXjBsvrMZgIAmGyvWL0kqkuKEzP3tB+L7cd7HD4AAAAAAEyQ4hjALLT1eG/s7O5LzDy7ZVEsKi/NbCYAgMm2oLQkXr2mKTX36a1tDh8AAAAAACZIcQxgFvranuRtY2OuWeGaSgBg9nvdupbxTapJvrnvcLT3DmQ2EwAAAAAAzAWKYwCzzPBofvzD0SQ1ZSXxrOa6zGYCYJoVlUZUtST/GcvALNRYWRYvWtGQmBnJ5+Oz220dAwAAAACAiSiZUBqAaXdv+7E4OjCUmHnBsvooK9YNBpgvcpVLovRp75vuMWDKvHFDa9yWsnH1i7s64i0bl41fbwkAAAAAAKTTKgCYZb62N/2ayqtdUwkAzCFraqriWc2LEjO9wyPxxZ3tmc0EAAAAAACzneIYwCxyYnA4vn/wSGJm+YKKOGfxgsxmAgDIautYmpu2t8XAyGgm8wAAAAAAwGynOAYwi9xxoCsGR/OJmWtWNEYul8tsJgCALDytoSY21lUnZrr6h+K2PR0eCAAAAAAAFEBxDGCOXVP54hUNmcwCAJClsWJ8IVvHPrnlYAyP2joGAAAAAABpFMcAZomDPf3x8OETqZs4WqsrMpsJACBLV7TWx9Lq8sRMW+9AfGtfV2YzAQAAAADAbKU4BjBLfH3v4dTM1SsbM5kFAGA6lBTl4k0blqbmPrHlQIzmk6/3BgAAAACA+U5xDGAWyOfz8bU9yddUlhfl4vlLF2c2EwDAdHjJysZorCxLzOw+0Rd3HjyS2UwAAAAAADAbKY4BzAKPHzkZ+3v6EzPPbV0cC0pLMpsJAGA6lBUXxRvWt6bm/uXJA+PlewAAAAAA4GdTHAOYBdK2jY25xjWVAMA88crVS2JRWXJhfsuxnvhR+7HMZgIAAAAAgNlGcQxghhscGY1v7z+cmFlcXhoXL1mU2UwAANOpsqQ4rl/fkpr7J1vHAAAAAADgKSmOAcxwdx86GieGRhIzL17RECVFucxmAgCYbteuaY7qkuLEzKNdJ+L+zu7MZgIAAAAAgNlEcQxghvt6AddUXr2iMZNZAABmioVlJXHt2ubU3D9u2hf5fD6TmQAAAAAAYDYpme4BAHhqxwaG4geHjiUe0bqaqtiwqNoxAsxj+b6OGN78N4mZko1vj1zlksxmgixcv64lbt7eFgMjo0+ZeeTft45dtKTWQwEAAAAAgJ+gOAYwg3173+EYSdmQcfVK28YA5r3RoYjetvQMzDGLK0rj1aub4qbtbalbx57RWBO5nKu9AQAAAADgP7iqEmAG+9reztQv4i9a3pDZPAAAM82bzmiN8qLkQth/bB0DAAAAAAD+f4pjADPUru7e2HS0JzFzcVNtNFaWZTYTAMBMU19RFq9e05yaG9s6lk/Z5AoAAAAAAPOJ4hjADPX1vYdTM9escE0lAICtYwAAAAAAMHGKYwAz0Gg+H99IuaayqqQoLm9dnNlMAAAzeevYqwrYOvYPto4BAAAAAMB/UhwDmIEe7OyO9r7BxMzzl9ZHRUlxZjMBAMxkb9rQGuVFucTMo10n4p72Y5nNBAAAAAAAM5niGMAM9JU9HamZq11TCQDwnxoqC9s69neP7x3f7goAAAAAAPOd4hjADHNyaDi+u78rMdNUWRZPa6zJbCYAgLmydWzr8d6440Dy91oAAAAAADAfKI4BzDDf3tcVA6P51G1jRbnkD0UBAObj1rFXF7B17KNP7IvhlO+3AAAAAABgrlMcA5hhvlrANZUvXdWYySwAALPNm89cGlUlyT/q7j3ZH7cV8D0XAAAAAADMZYpjADPIru7eePzIycTMBQ0LY/mCysxmAgCYTerKS+OG9a2puY9t3h8DI6OZzAQAAAAAADOR4hjADPLVPZ2pmZetXJLJLAAAs9Xr17dETVlJYqajbzC+sPNQZjMBAAAAAMBMozgGMEMMj47G11KKY5XFRfH8ZfWZzQQAMBstKC2JN5+xNDX3L08eiJNDw5nMBAAAAAAAM43iGMAMcc+hY3FkYCgxc9Xy+qgqKc5sJgCA2eratU3RWFmWmDk2OByf2HIgs5kAAAAAAGAmURwDmCG+sqcjNfNS11QCABSkorg4fvHMZam5m7e1RVvPgFMFAAAAAGDeURwDmAGO9A/F3W3HEjPLF1TE+fULM5sJAGC2e9mqxlhWXZGYGRzNx989sTezmQAAAAAAYKZQHAOYAb65rzNG8vnUbWO5XC6zmQAAZruSoqL41bOXp+a+ue9wbDpyMpOZAAAAAABgplAcA5hm+Xw+vrK7I/WL9TUrGzKbCQBgrrhqWX2cvXhBau5Dj+0e/74MAAAAAADmC8UxgGn25LGe2NHdl5h5ZtOiWFJZntlMAABzxdjG1v9x7srU3MOHT8T3Dh7JZCYAAAAAAJgJFMcAplnatrExL1u1JJNZAADmovMbauJ5Sxen5j782N4YGh3NZCYAAAAAAJhuimMA02hgZDS+te9wYqamrCQua6nLbCYAgLno7eesjJJcLjGzv6c/btrWltlMAAAAAAAwnRTHAKbR2HVIJ4ZGEjMvXt4QZcW+XAMAnI5lCyritWubU3P/tHl/tPcOOGwAAAAAAOY8TQSAGX5N5UtdUwkAMCl+YePSqCktTsz0jYzGhx/b48QBAAAAAJjzFMcApsmh3oH4ccfxxMyG2qo4Y1F1ZjMBAMxltWWl8ZaNy1Jz397fFfenfJ8GAAAAAACzneIYwDS5bU9n5FMyto0BAEyusesqVy2sTM39n0d2xfDoqOMHAAAAAGDOUhwDmAaj+Xzctif5msrSoly8eHlDZjMBAMwHJUVF8a4LVqfmdnb3xa07DmUyEwAAAAAATAfFMYBp8PDh7jjQM5CYuaylLmrLSzObCQBgvrhoSW1cubQ+NfcPm/ZHZ99gJjMBAAAAAEDWFMcApsG/7U7eNjbmZauWZDILAMB89D/OWxkVxck/EvcOj8RfPLwrs5kAAAAAACBLimMAGTs+OBR37O9KzDRWlMYzmxZlNhMAwHzTVFUev3DmstTcnQePxHcPJH/vBgAAAAAAs5HiGEDGvrH3cAyO5hMzV69sjOJcLrOZAADmo9evb4nlCypSc3/+8K44MTicyUwAAAAAAJCVXD6fT24vADBpxr7kvv47j8TO7r7E3K0vvCBWLKx08gAAU+yeQ0fjHT94MjX3ilVL4j1PX+t5AAAAAAAwZ9g4BpChx4+cTC2NPb2xRmkMACAjlzbXxQuW1afm/m13RzzQeTyTmQAAAAAAIAuKYwAZ+uKu9tTMK1c3ZTILAAD/zzvPXx01ZSWpx/H+B3ZG/8iIYwMAAAAAYE5QHAPIyInB4fjO/q7ETG1ZSVzRutgzAQDI0OKK0njHeStTc/t7+uMjj+3NZCYAAAAAAJhqimMAGfnmvsMxMDKamHnJysYoK/alGQAga9esaIyLl9Sm5m7ZcSjuaz+WyUwAAAAAADCVtBMAMpDP5wu6pvLlq5Z4HgAA0yCXy8XvX7gmygso8f+vB3aMb5MFAAAAAIDZTHEMIAObjp6M7cd7EzMXNCyM1TVVngcAwDRZuqAifuWs5am5jr7B+IuHd2UyEwAAAAAATBXFMYAMfGlXR2rmFauaPAsAgGn2unUtcVZddWruG/sOx3f2H85kJgAAAAAAmAqKYwBTbOwao2/uS/5QcWFpcTx/2WLPAgBgmpUU5eLGi9YXdGXlBx7cGe29A5nMBQAAAAAAk01xDGCKfW1vZwyMjCZmrl7RGBXFxZ4FAMAMsHJhZfzGuStTc91DI/FH922L4dF8JnMBAAAAAMBkUhwDmEL5fD6+sLM9NffK1a6pBACYSa5d0xTPXFKbmnuk60R8dNPeTGYCAAAAAIDJpDgGMIUe6OyO3Sf6EjPn1y+MtbVVngMAwAySy+XiD5+xNmpK07fCfnLLwfhB29FM5gIAAAAAgMmiOAYwhQrZNvaatc2eAQDADLSksjx+98I1BWVvvH97tPcOTPlMAAAAAAAwWUom7W8C4L843DcYdx48kngqdeUl8bzWxU4OgNOSHzgSIztvScwUr7kucuXec2CiXrC8Ie5uOxrf2Hc4Mdc9OBx/cO/W+PvLz46SIr+jBQAAAADAzKc4BjBF/m13R4zk84mZl61aEmXFPlgE4DQN90W+64HkzIqXRZQ7aTgVY1vHNh09GXtP9ifmHjtyMv7qkd3xOwVuKQMAAAAAgOmkrQAwBYZH8/GlXcnXVOYi4lWrm5w/AMAMV11aHO+/ZEOUF419B5fsczvbC7quHAAAAAAAppviGMAU+MGho9HRN5iYeVbzomitrnD+AACzwPra6njXBasLyv7Fw7vioc7uKZ8JAAAAAABOh+IYwBT43I5DqZlXr2l29gAAs8jYNeNXr2hIzY1dV/77P9oSB3uSr7YEAAAAAIDppDgGMMl2dffGfR3HEzMtVeVxafMiZw8AMIvkcrn43QvXxKqFlanZY4PD8Tv3bIne4ZFMZgMAAAAAgIlSHAOYZLcWsG3slaubojiXc/YAALNMVUlxfOCSM6K6pDg1u/14b7znR1tjeHQ0k9kAAAAAAGAiFMcAJtHJoeH42p7OxExpUS5evmqJcwcAmKVW1VTG/7p4fRTyawD3tB+L9z+4M/L5fAaTAQAAAABA4RTHACbRV3Z3Rt9I8kaJFyxriMUVpc4dAGAWe3ZLXbztnBUFZW/b0xkf3bRvymcCAAAAAICJUBwDmCQj+XzcuqMtNXfdumZnDgAwB7xxQ2u8eHlDQdl/fvJAfGFn+pXmAAAAAACQFcUxgElyz6FjcaBnIDFz7uIFsbFugTMHAJgDcrlcvPvpa+KsuuqC8n/+0K64fX/XlM8FAAAAAACFUBwDmCSf3V7ItrEW5w0AMIdUFBfHBy89M5qrylKzYxea/9F92+L7B49kMhsAAAAAACRRHAOYBLu6e+O+juOJmcaK0nj+0sXOGwBgjmmsLIu/fvbGqCktLuh68/fcuzXuOXQ0k9kAAAAAAOCpKI4BTIJbdxxKzbx6TXOUFPmyCwAwF62uqYo/f9aZUV6US80Ojebj9+7ZEven/OIBAAAAAABMJQ0GgNN0fHAobtvTmZgpLcrFK1c3OWsAgDnsgoaaeN/F6yO9OhYxMJqP3/7hk/FAp/IYAAAAAADTQ3EM4DR9cWd79I+MJmZeuLwhFleUOmsAgDnuiqX18a4LVheUHfse8rfu3uzaSgAAAAAApoXiGMBpGBwZjVsKuKbytWubnTMAwDxx7drm+NWzlxeUHds89q4fbonvHuia8rkAAAAAAOAnKY4BnIZv7TscXf1DiZnz6hfGxroFzhkAYB75hTOXxS+cubSg7HA+H39w79b4+t7k688BAAAAAGAyKY4BnKJ8Ph83bWtLzb1xfaszBgCYh37lrOXxxg2FfS84ko9474+3x63b07+/BAAAAACAyaA4BnCK7u04Htu7exMzy6or4jmtdc4YAGAeyuVy8fZzVsR1BV5bno+Iv3hkd3zksT0xmh/7bwAAAAAAMHUUxwBO0We2HkzN3LC+JYpzOWcMADCPy2PvPH9VXLumqeDXfHLrwXjv/dtjaHR0SmcDAAAAAGB+UxwDOAXbjveMbxxLUlNWEi9d2eh8AQDmubHy2LsuWF3wtZVjvrH3cLzzB0/GyaHhKZ0NAAAAAID5S3EM4BTctK0tNfOaNU1RUVLsfAEA+M9rK3/prGUFn8Z9Hcfjl+58PA729DtBAAAAAAAmneIYwAS19w7EN/ceTsyUFuXitWubnS0AAP+lPPbWjcvjN89dWfCp7Ozui1+447F4+HC3kwQAAAAAYFIpjgFM0Ge2tcVwPp+YedHyhqivKHO2AAD8N2/Y0Brvftqagn8gPzY4HG+/a1PctqfDaQIAAAAAMGkUxwAm4NjAUHxpV3tq7vXrW50rAABP6ZWrm+IDl54R5cWF/Vg+NJqP992/I/76kd0xPDrqZAEAAAAAOG2KYwAT8NntbdE/kvxB3aVNi2JtbZVzBQAg0XNbF8dHLjsrastKCj6pm7a3xW/ctTm6+gedLgAAAAAAp0VxDKBAPUMjceuOQ6m5N5+x1JkCAFCQc+sXxseuOCdaq8oLPrEHD3fHm29/NB7tOuGUAQAAAAA4ZYpjAAX64q72ODE0kpg5r35hXNCw0JkCAFCwFQsr42PPOyfOXbyg4Nd09g/Fr33vifFfbMjn804bAAAAAIAJUxwDKMDAyGjctO1gQdvGcrmcMwUAYELqK8riI889O168vKHg1wzn8/EXD++KG+/fHv3Dyb/gAAAAAAAAP01xDKAAt+3pjMP9Q4mZdbVV8ezmRc4TAIBTUl5cFDdetC5+9ezlE3rdN/Yejl+88/HYf7LfyQMAAAAAULBc3p0WAImGR/Nx3bceigM9A4m59128Pl40gQ0RADBZ8qNDEX0dyaHKJZErKnXoMEvccaAr3vfj7dE3MlrwaxaWFscfP2NdXNa6eEpnAwAAAABgblAcA0hx256OeN/9OxIzS6vL45YXXhglRa6pBABgcuzs7o3fvWdL7JvgJrHXr2+JXz9nRZQWWTIOAAAAAMBT82+RAVK2jf3T5v2pZ/TGDUuVxgAAmFRraqriX55/blzeWjeh131mW1v88p2PxwFXVwIAAAAAkEBxDCDBN/Z2xv6UKyrrK0rjJSsbnSMAAJNuQWlJ/NklZ4xvEJvID/CbjvbEm25/NG7f3+WpAAAAAADwMymOASRsG/vnJ9O3jb1hfWuUF/tyCgDA1CjK5eLNZyyNDz1nY9SWlRT8up7hkXjPvVvjAw/ujP6REY8HAAAAAID/QtMB4DS2jdWVl8Zr1jQ5QwAAptzFTYvik1eeFxvrqif0ui/sao9f/O7jsbu7b8pmAwAAAABg9lEcA/gZhkdH458K2Db2cxtao6Kk2BkCAJCJ5qry+Ojl58QrVi2Z0Ou2H++NN9/xaHxtT+eUzQYAAAAAwOyiOAbwM3x97+E4kLJtbHF5abzatjEAADI2dk36e56+Nv7o6WujYgJXpvePjMZ7798e7/3x9ugddnUlAAAAAMB8pzgG8DO2jf1zIdvGzrBtDACA6fPSVUviX55/bqytqZzQ6762tzN+/vZHY9vxnimbDQAAAACAmU9xDOCnfHl3R0Hbxl61usnZAQAwrVbXVMU/Pf/ceOXqiV1duedkf7zljsfiCzsPRT6fn7L5AAAAAACYuRTHAH5C//BIfGyzbWMAAMweFcXF8e6nrY3/ffH6qCopLvh1g6P5+MBDu+L3f7Q1jg8OTemMAAAAAADMPIpjAD/hszsORVd/8odm9RWl8ao1to0BADCzvGB5Q3zyynPjzEXVE3rdnQePxJu+82g8dLh7ymYDAAAAAGDmURwD+Hfdg8Pxr1sOpJ7HmzYsHd/qAAAAM83yBZXxj1ecE9eva5nQ69r7BuPXv/dEfGzzvhhxdSUAAAAAwLyQy+f9G2GAMX/z2J74160HEw+juaosbnnhhVFerHcLwMyRH+yO0bY7EzNFLVdErqwms5mA6fe9g0fif9+/PbqHRib0ugsbFsZ7L1ofTVXlUzYbAAAAAADTT3EMICI6+gbi2m88FAOj+cTz+KOnr42XrlrizACYUfI9B2L4oRsTMyUX3hi56qWZzQTMDId6B+KP7tsWj3admNDraspK4g+ftjYuX7p4ymYDAAAAAGB6WZkDEBEf37w/tTS2emFlXL2y0XkBADBrNFeVx98996x48xlLJ3yN++/+aEt88KGd0T8ysY1lAAAAAADMDopjwLy3u7svvrK7I/Ucfu3sFVGcy8378wIAYHYpKSqKXz9nRXzoORujrrx0Qq/9/M72+MU7Ho+d3b1TNh8AAAAAANNDcQyY9z782J4YSV42FmcvXhDPba2b92cFAMDsdUnTovj0VefFJU21E3rd9u7e+Pk7Hosv7myPfD7lG2cAAAAAAGYNxTFgXruv/Vjcfehoau5t56yInG1jAADMcvUVZfFXz94Yv3nuyiiZwPe3AyOj8WcP7Yz33Lt1/BpLAAAAAABmP8UxYN4ayefjQ4/uSc2NbWR4euPEtjIAAMBMVZTLxRs2tMbHnndOLKsun9Br7zhwJN50+yPxaNeJKZsPAAAAAIBsKI4B89aXd3WMX7uTZGwHw6+fszKzmQAAICsb6xbEJ688P168omFCrzvUOxi/+r3H45827x//ZQwAAAAAAGYnxTFgXjo5NBwf3bQvNfeSlY1xxqLqTGYCAICsVZcWx3svWh9//Ix1UVVS+L8iGMnH+PfTb//+pmjvHZjSGQEAAAAAmBqKY8C89IktB+LowFBiprK4KH7t7BWZzQQAANPlmpWN8YnnnxdnTvCXJh483B1v+M4j8a19h6dsNgAAAAAApobiGDDvHOzpj5u3taXmfu6MpdFQWZbJTAAAMN1WLKyMjz3vnHjD+pYJve7E0Ej80X3b4o/v2xYnBoenbD4AAAAAACaX4hgw7/zlI7tjcDSfmGmqLIvXb5jYB2YAADDblRYVxW+etyr++tlnRl156YRe+419h8e3jz3QeXzK5gMAAAAAYPIojgHzyl0Hj8RdbUdTc287Z0VUFBdnMhMAAMw0lzbXxaevOi8uXlI7ode19w3G276/KT782J4YHBmdsvkAAAAAADh9imPAvNE/MjK+bSzN2YsXxAuXN2QyEwAAzFT1FWXxoedsjLefsyKKc7mCXze22/dTWw/GW777WOw43julMwIAAAAAcOoUx4B545NbDsbB3oHU3DvOWxW5CXwwBgAAc1VRLhdvOmNpfOyKc2JZdfmEXrvteG/8/B2PjpfIRvLJV8UDAAAAAJA9xTFgXth3si/+dcuB1NxLVjbGefULM5kJAABmi7MWL4hPXHleXL1iYpt5B0fz49dWvtX2MQAAAACAGUdxDJjz8vl8/J+Hd49/aJVkQWlxvO2cFZnNBQAAs8mC0pK48aL18SfPXB81pcUTeu2moz3xc7c/Gh/btC+GRkenbEYAAAAAAAqnOAbMed89eCTuaT+WmvvVs1dEfUVZJjMBAMBsddWyhvj0C86Pi5fUTuh1w/l8/OPm/fHm2x+NTUdOTtl8AAAAAAAURnEMmNO6B4fjLx7elZo7Y1F1vHpNUyYzAQDAbLeksjw+9JyN8VvnrYqyotyEXrujuy9+8buPxYce3R39wyNTNiMAAAAAAMkUx4A57f8+tju6+odSc79zweoozk3sAy8AAJjPinK5uH59S/zL88+L9bVVE3rt2GWVn9nWFm/4zqNxf8fxKZsRAAAAAICnpjgGzFk/7jgeX9ndmZp7+aolcW79wkxmAgCAuWZtbVX80/POjTduaI2J/irG/p7+eNtdm+IP7t0a7b0DUzQhAAAAAAA/i+IYMCeNXXnzpw/uSM3VlJXE285ZkclMAAAwV5UVF8VvnLsy/va5Z8Wy6vIJv/47+7vidd96OD655UAMjY7tIwMAAAAAYKopjgFz0j9s2hcHetI3FrzjvJWxqLw0k5kAAGCue1pjbXz6qvPjDetbJvwvHPpGRuMjj++N67/1cNy+vyvy+fwUTQkAAAAAwBjFMWDO2XTkZNy0rS0198wltXHNisZMZgIAgPmioqQ4fvO8VfGx550Ta2sqJ/z6/T0D8Z57t8Yv3vl4PHy4e0pmBAAAAABAcQyYY/pHRuK992+PtMttKoqL4veftiZyuVxGkwEAwPxy9uKF8Ykrz4u3blwWJafwffcTR07Gr3zvifjtHzwZm4+enJIZAQAAAADmMxvHgDnl7x7fF7tP9KXmfvXsFdFaXZHJTAAAMF+VFhXFL521PD5x5blxVl31Kf0ddx86Gj9/x2Pxzh9sHt8uDAAAAADA5FAcA+aM+zuOx83b06+oPLtuQVy3rjmTmQAAgIh1tdXxj1ecG79x7srx7b+n4geHjsUvfPex+I27NsUPDx2N0Xze0QIAAAAAnIaS03kxwExxcmg4/tcD21NzxblcvOfpa8b/CQAAZKekKBdv3NAaVy2rj//76J64/UDXKf0993UcH/+zamFlvG5dS1yzoiEqSoonfV4AAAAAgLnOxjFgTvjLR3bHod7B1NxbNi4d33YAAABMj+aq8nj/JRviby47a7z8darGrqj/wEM745rbHog/e3BnPHHkRORtIQMAAAAAKJiNY8Csd+eBrrhtT2dq7qy66vj5M5ZmMhMAAJDsoiW18emrzovP7WiPjz+5P7oHh0/pyHqGR+KLu9rH/6ypqYwXr2iM57UujhWnUUoDAAAAAJgPcnm/jgvMYod6B+JN33kkuodGEnPlRbn45JXnx6oaHx4BMPfkew7E8EM3JmZKLrwxctUK1MDMdGJwOD655UDcvL0tBkfzk/J3rqupiuctXRzPaamLDYuqo8h19QAAAAAA/4XiGDBrDY/m49e+/0Q82nUiNfvO81fF69a1ZDIXAGQtP9wb+WObEjO5RWdFrqQqs5kATvUXQ/5h0774xt7OGJmc/ti4RWUl8YwltfHMJbVxQUNNLF9QETlFMgAAAABgnlMcA2atjz6xN/7pyQOpuWc01sSHLzvLhgEAAJgl9p/sj39+cn98fZILZP+htqwkzl68YPzPGbXVsba2Kpqryv3MAAAAAADMK4pjwKx0f8fxePtdmyLtM6TqkuL4zAvOH/8QCAAAmF0OnOyPf9lyYLxANjRJV1g+lcriolhdUxnLF1RGa3V5LK2uGP9nY0VZ1FeURVVJkS1lAAAAAMCcojgGzDpHB4bijd95JA73D6Vmb7xoXVy9ojGTuQAAgKnR1T8Yn9/ZHl/YeSiODgxPyzGXFxdFfXlp1FeUxuKK0qgvHyuUlcai8tLxDWbjf8pLx6/FHPvPFSXF0zInAAAAAEChFMeAWWUkn4/funtz3NtxPDX7kpWN8T+fsS6TuQAAgKk3MDIa39zbGZ/b2R5bjvXM6CMvL8qNF8n+s1RWNlYyKxkvmjVUlMWSyrJoqCiNxsqyWFxeapsZAAAAAJA5xTFgVvn7J/bGPz95IDW3YkFFfOLK86LKb/kDAMCctPVYT3x1T0d8fe/h6B6cni1kk6WiuCiWVpdHa3XF+BWZY1dmrq2pGv/ngtKS6R4PAAAAAJijFMeAWeOug0fiXfdsSc2VFuXi4887N85YVJ3JXAAAwPQZHBmNHxw6Gt89cCTuajsavcMjc+pxtFSVx/raqjinfmGcs3hBbKxb4BdkAAAAAIBJoTgGzAr7TvbFz9/xWJwcSv8Q6J3nr4rXrWvJZC4AAGBmXWX5447jcceBrri3/Vgc7h+KuaYoItbVVsXFTYvi4iW1cX7DwqgoLp7usQAAAACAWUhxDJjx+odH4hfvfDy2H+9NzV7WUhd/fukZkcvlMpkNAACYmfL5fOzs7ov7Oo7HfR3H4uHDJ+bcNrIx5UW5OL+hJi5vXRxXtC6Ohsqy6R4JAAAAAJglFMeAGf9hz//88bb41r6ugq5w+cSV50ZtWWkmswEAALPHSD4fe070xeNHTsbjXSdi89GTsftEXwyO5mOuGPv1mbENZM9rrY+rltUrkQEAAAAAyf9OMT/WygCYof7lyf3xd0/sS82VFeXiH684J86sW5DJXAAAwOw3PJqPAz39saO7N3Ye7439Pf1xoGcgDvb0z/prLotzEc9qrouXrVoSz25eFCVFY5dcAgAAAAD8/xTHgBnrzgNd8Xs/2lpQ9g+fvnb8AxEAAIDJ0D88Ml4eOzIwFF39g9H1E//5SP9QdA0Mjf/z+ODwjL8Cs76iNF66cklcu7YpllSWT/c4AAAAAMAMoTgGzEhbj/XEL9/5ePSNjKZmX7l6Sbz7aWszmQsAAOCnDY2ORvfgcBwbGI7jg/+vTHb8p//7wHAcGxwrng1FZ99gDE/DAvjiXC5euLw+bljfGmcsqvYgAQAAAGCeUxwDZpyx39r/he8+God6B1OzG+uq46OXnxPlxa5dAWD+yg/3Rv7YpsRMbtFZkSupymwmAJ7aaD4/Xibr6BuMtn+/HnPsysz9J/tj14m+8f/7VHt6Y0384sZl8fTGWo8KAAAAAOYpxTFgRukfGYm3fX9TPH7kZGq2rrwk/vl550VLtatWAJjf8j0HYvihGxMzJRfeGLnqpZnNBMCpG9tetrO7N7Yf741NR0/G410nYs/J/ikrkP3SWcvjwoaaKfn7AQAAAICZq2S6BwD4DyP5fPzxfdsLKo2V5HLxgUvOUBoDAADmnJqykrigoWb8z0+WyR7rOhE/7jge93Ucix3dfZPyv/VAZ3c88L0n4uIltfHr56yIjXULJuXvBQAAAABmPsUxYMb40KO7486DRwrKvvtpa+J8vxEPAADMozLZs1vqxv+M6ewbjHvaj8WdB7rivo7jMTSaP62/f+zvuO+Ox+KaFY3xq2cvj6Yqm50BAAAAYK5THANmhJu2tcVntx8qKPv69S3x0lVLpnwmAACAmaqxsixevmrJ+J+TQ8Nxd9vR+Pa+rrin/WiMnEaH7Gt7O+P2A13xxg2t8aYNrVFZUjyZYwMAAAAAM0gun8+f3q+kApymOw50xXt+tDUK+WJ0adOi+D/PPjOKcznnDgD/Lt9zIIYfujHxPEouvDFy1UudGcAcN7aJbKz89ZXdHbHvZP9p/V1NlWXx2xesjstbF0/afAAAAADAzKE4Bkyr+zuOxzt+sLmga1XW1FTGP15xTiwotSwRAH6S4hgAP23s9wTv7+yOz2w7GD88dOy0Duiylrr47fNXR0u16ysBAAAAYC7RvgCmzeajJ+N37nmyoNJYQ0Vp/NWzNyqNAQAAFCCXy8VFS2rH/+zq7o2bt7fF1/Z0xmABP3/9tLvajsaPO47HWzcuixvWt0ZJkQ3QAAAAADAXFE33AMD8tLu7L95x9+boHR5NzVaVFMVfPntjNFf57XYAAICJWl1TFe9+2tr4/IsvjNeubY7SUyh+9Y+Mxt88vjd++XuPjxfRAAAAAIDZT3EMyFx770D85t2b4tjgcGq2OBfx/mduiDMWVWcyGwAAwFy1pLI83nXB6vj8iy6M16xpipLcxAtkTxw5GT93+6PxyS0HYvgUtpcBAAAAADOH4hiQqa7+wfiNuzZFe99gQfnfu3BNXNpcN+VzAQAAzBdNVeXxuxeuiZtecH5c0bp4wq8fu+7yI2Pbx+58PPae6JuSGQEAAACAqac4BmTm2MDQeGlsz8n+gvJv3bgsXrG6acrnAgAAmI9WLKyMD1x6Rvztc886pS3PTxw9GW+6/dH44s72yOdtHwMAAACA2UZxDMjEicHh+M27N8eO7sJ+G/21a5vHi2MAAABMrac31sa/PP/c8Y3PC0uLJ/Ta/pHR+LOHdsbv3LMljg4MTdmMAAAAAMDkUxwDplzP0Ei84webY8uxnoLyL1xeH+88f1Xkcrkpnw0AAICIolwuXr2mKW554YVx9YqGCR/JXW1H4/XffiR+3HHccQIAAADALKE4Bkyp3uGReOcPN8fjR04WlL+0aVH8z2esG//QAgAAgGwtriiNGy9aHx+57KxYVl0xodceGRiK37hrU/zjpn0x4upKAAAAAJjxFMeAKS2N/dYPNsfDh08UlD+vfmH82SUborTIlyYAAIDp9IwltfHpq86LG9a1xER+rScfER/bvD9+865N0dU/OIUTAgAAAACnSzsDmLrrKe8uvDR25qLq+KtnnxkVJcWeCAAAwAww9vPZO85fFR+9/OxYvmBi28fu7+yON93+aNzv6koAAAAAmLEUx4ApKY2NbRp7pKuw0ti6mqr4v8/ZGAtKSzwNAACAGeb8hpr41JXnxXVrmyf0uq7+/3d15cc373d1JQAAAADMQIpjwKQ6OTQc75hAaWzVwsr4v5dtjNryUk8CAABgBm8f++0LVo9vil48gZ/fRiPiHzbtG99IfaR/aEpnBAAAAAAmRnEMmDTHBobibd/fFI8WWBpbWl0eH75sY9RXlHkKAAAAs8CzmuviMy84Py5rqZvQ6+7rOB5vuv2ReOhw95TNBgAAAABMjOIYMCkO9w3Gr33/iXjyWE9B+daq8v+vvfuAjqM6/z7+qPfmJvfeC7bBFBe6HSBgwBhCgFBCJ7RQQwgBU8I/Ly1AgBACAUIgoZhAAGNqMLjgAgbcey+ybMvqdbXvea4kI8tbpS2zM9/POXNW2tmdvTuzezW6+9vnytNHD5NOaSkcAQAAAACIIXkpSfLw2EFy66g+khQfF/D9dlfpl42Wyb/W7BC32x3WNgIAAAAAAADwLzGA2wCATzvKq+W6r5bL1vKqgENjfzl2mHROJzQGOEFZWZl8//33smzZMtm6davs2rVLqqqqxOVySWpqquTk5Ei3bt2kf//+Mnr0aOnevXu0mwwAAAA/4uLi5Jx+nWV4u0y58+vVsr2iOqB95nKLPP7DRlm2t1TuPKyfpCcmsK8BAAAAAACAKIlz8xVPAG2wubTShMYKKmsCnp7ymWMIjQFOUFBQIO+8847MnTtXamtrA76fBsgmT54shx9+uNjdxo0b5fe//70J0Xlz1VVXybHHHtvmx7r//vtlxYoVEm6vvPKKJCTwAXCkucu3Sd3iaT5vkzh6msRldItYmwAAzlFaUycPfLNOvti+N6j79c1Ok/931CDpmZUWtrYBAAAAAAAA8I6pKgG02rriCrlq1jJCYwAOoJl0DYzdfvvtMmvWrKBCY2rt2rXypz/9Sf7v//5PioqKbLt3NSz23HPP+QyNAQAAxIKs5ET541ED5eaRvSUxLvCpK9eXVMolny+RWUEGzgAAAAAAAACEBsExAK2yoqhMrv5ymeytDiwQ0iMzVf5CpTHA9qqrq+WRRx6RN954I+jAWEtLliyR3/3ud7J+/Xqxo/fff99UHAMAALDL1JXn9u8izx03TLqkpwR8v/I6l9w+b5U8s3SzuNzusLYRAAAAAAAAwIEIjgEI2ne7S+RXXy6Xkpq6gG7fLztN/nrsMMkP4sMDALGnpqbGhMYWL14csm3u27dPHnzwQdsFrLZv3y5vv/12tJsBAAAQcsPaZck/TjxEjumSF9T9Xl61TX49e4XsC/DLSQAAAAAAAADaLjEE2wDgIHN3FskdX6+Wald9QLcfkpchT4wfIjkpSWFvG4Doeumll2TZsmVe13fp0kWOP/54GTp0qHTs2FESEhKktLRU1q1bJ3PnzjWBM53msqWKigoTSNMAWXZ2tsQ6fY5/+9vf2lyRDQAAwKqykxPlobGD5NU1O+SZpZvEFWAhsQW7iuXiz3+QPx41SIbkZYa7mQAAAAAAAIDjERwDELAPNxfK/YvWBTx9yKgOWfLouMGSmURXA9idBr+++OILj+s0IHbOOefIqaeean5uLj09XfLz82XcuHGyZs0aeeqpp6SwsPCgbezdu1f++te/ym233Sax7uOPP5ZVq1YdcF18fLzU1wcWyA21O+64QwYPHhyy7bU8xgAAwLlTV/5iYFcZnJshdy1YLUXVgVWs3llRI1d+sVRuG9VHTu+TH/Z2AgAAAAAAAE7GVJUAAvKvNTtk2sK1AYfGjuyUYyqNERoD7E8rgv3zn//0uE4DUdddd52cfvrpfgNFAwYMkHvvvddUJvNEK5ItXLhQYpmG4l5//fWDrj/llFMkWhITEyU5OTlkCwAAQHNjOuXIyyccIsPbBV5BrKbeLX/4dr08+M26gKtdAwAAAAAAAAgewTEAfqdUe2bpZnn8h40B76lju+bJI+MGS2oiVWcAJ5gxY4bs27fP47qpU6fKkUceGfC2cnNz5eabb5aUlBSP6//1r39FrTJXKLzwwgtSVVV1wHX9+/eXiRMnRq1NAAAA4ZafniJ/OWaYTO0bXAWxdzfukqtmLZUd5dVhaxsAAAAAAADgZATHAHhVV++WB79dLy+v2hbwXjqpRwd58MiBkpxA9wI4gYagdOpFT7p3724qjQWrW7ducuaZZ3pct3PnTlmwYIHEolmzZskPP/xwwHVahe2KK64wldkAAADsTP9HvH10X7lnTH9JiY8L+H4risrl4s9/kPkFnr+oAAAAAAAAAKD1EttwXwA2ptOB/H7Bapm1vSjg+5zRu5P85tC+khAX+IcAAGLbvHnzpKyszOO6s88+2+/0lN7o1I1ayay0tPSgdZ9++qkcddRREku0Ipun6TwnT54sPXr0MFNYAm2SlCXxPSb7vQ0AANH2014dpX9Ouvxm3irZXhFYJbHimjr59ewVctWwnnLRoK4Sz/+cAAAAAAAAQEgQHANwkLLaOrlt7ir5dndJwHvnggFd5PoRvSSOAXzAUebMmePx+nbt2smYMWNavd3k5GQ5/vjj5b///e9B61asWCG7d++WDh06SKx48cUXpby8/IDrOnfu7LWyGhCsuORsSegVfIU/AACiYWBuhrx04gi5Z8FamRdgJTGdrPwvyzbLsr2lcs/h/SUziSEtAAAAAAAAoK0YZQNwgD1VNeab3KuLKwLeM9cN7ykXDurGngQcRquBaYjLk7Fjx7Z5+sXx48d7DI653W5ZtGiRnHzyyRIL5s+fLwsXLjzo+ssuu8wE5GAt9fX15nX93XffyYYNG8z0qBr6q6urk7S0NBOK7Nu3r4wePVoOPfTQoKvq6fSu3377rSxdulQ2bdoke/bskcrKSrOdnJwcs/1hw4aZ4GXPnj0lUqqrq02bVq9eLRs3bjRV8EpKSsz1GgpPTU2VvLw86dKliwwYMEBGjRplppUNt4KCAtOmbdu2mUV/1+Oh+1HblpiYuL9t+fn50rt3b7P/+vXrF/UpYCsqKszrSKeo3bx5swm86rFOSkqSrKwsc7z1tTRy5EgZOnSopKSkRLW9ABBpOclJ8tj4wfLCiq3y/IqtAd/vyx1FcsnnS+T/HTVI+uWkh7WNAAAAAAAAgN0RHAOw36bSSrlx9grZEeB0IQlxInce2k9O692JvQg40LJly0yIyxMN1LSVTuGoVcU0bNHSkiVLYiI4ptN4vvTSSwddf+yxx5pwC8Jv1qxZ8te//vWg64855hi5+uqr9/+ur+UvvvjChBU1nOTteOqiISC9rYaVzjvvPJkwYYLfdmgI67333jNTrWrgqaXa2loThtLH1uDaW2+9JSNGjJBLLrnEhLXCRZ/LBx98IAsWLPDYrpbPfcuWLea2r776qgk9nX766XL44YeHrOJoTU2NfP/99yYcunz5chOs83d7XXT/ahBP26Y0gKdVC7WfyMjICEnbbrjhBo/90RNPPCEdO3bc/7vup3feeUc+//xzc0xbcrlc5noN561du1Y+/vhjyczMlClTpsikSZNMGA4AnEKnnLxiaA8Zkpcp0xaukdJaV0D321JWJZf+b4ncdVg/mdQjdqrQAgAAAAAAAFbDpxIAjCV7SuWWuSuluKYuoD2SEh8nfzhyoBzdtR17EHAoDXV4otV0tCJRKGgVni+//PKg6zVYo5Whol1RyJ9XXnlFiouLD7guOztbLrjggqi1CQcrKiqSJ598UlatWhX0/Z555hlTQUxDaN4qyC1evNiE1zTcFAwNSN5xxx1y5ZVXmgp8oaRtee211zy+vwK1fv16efzxx8379IorrjAVv9riueeeMxX6tCpXW+3du1emT58uH330kVx00UUBhftCQV8L+jyCPdYaNtP+QsNmeszbt28ftjYCgBVN6JInL51wiNzx9SpZE2D16ypXvdy1YI0s3Vsm143oKUkWPy8EAAAAAAAArIhRNQDy1fa9cu1XywMOjWUmJciTRw8lNAY4nIZGPNHp9UJVMUenm/NEq/Xs2LFDrEyrJn311VcHXa8hFq0uBGvQ6Q9///vfBx0aa+7rr7+Wxx57zIQZW5o5c6Y88sgjQQeJmlci+8tf/iJz586VUNHgpYaT2hIaaxkiveuuu0wVwraYN29eSEJjLQNZGu578cUXPR6fUPrwww/l0UcfbfWxbno93nvvvV6r3gGAnXXPTJXnjxsup/QMroLYv9fukCu/WCrbyg6u8ggAAAAAAADAN4JjgMO9s6FAbp+3SqpdgX2Y2iE1SZ49dpiM6pAd9rYBsC4NYOiUdd6CY6Hia1s6LZ1VabDthRdeOOj6kSNHyrhx46LSJniuSvXHP/7RXLbVDz/8IP/+978PuO6TTz6Rf/zjH16ndA3m/aYVy0IRltSKXg8++KDs27dPQqm8vFweeughUyXNivRYaEWvcG+/rcda6XSYOv2lTmkJAE6Tmpgg94zpL7eN6iOJQUyDvLyoXH7x2Q/y0ZaDpxQGAAAAAAAA4B1TVQIOpR9sPr9iq1kC1T0jVf589BDpmpEa1rYBsL49e/aYSkiedOnSJWSP07lzZ6/rdu7cKVb1r3/9y4Q/mktJSZFLL71UrEb3owaStOKWhgG1QlNpaakJrejUi1odTafN6969u/Tt21dGjBhhi2n0NIz11FNPmddyc926dZPDDz/cPM927dpJVlaWCQLq8dRw2BdffOE1aDZjxgwzJaIGHrWql4bGmouLi5NRo0aZpX///pKTkyOpqalmf+u+X7hwocyZM8djZSx9v2nVrDvvvLPVz1mnzPzzn//ss/KWHmMNOA4ZMsQcZz3+2m6dcnX79u1mGwsWLJCKigqPbdSpK++//37p2rWrhIL2Jzr1re5TXXJzcyUtLU3S09Olrq7OtEOPoVZAXLp0qQmueQtv6bSVut9DPe2nHuuXX375gOt0nw0bNszsy0GDBpljrfuyqb36WtKKby37iSYbN26U999/X84444yQthUAYoH2oWf36zFSz2AAAHKtSURBVCyDcjPkt1+vksIqz+ecLVXUueTuBWtkQcE+uXVUH0lLTAh7WwEAAAAAAIBYR3AMcKC6erc8tHi9vLtxV8D30UH7x8cPkXapSWFtG4DYsGuX9/6jY8eOIXscDVto4Kq6ujqoNkTTypUr5dNPPz3o+rPPPjuk+yZUnn/+ea/rdNpAXQoLC83zah4uOvHEE+Xoo48O2bSkkaYhreavq+zsbPn5z38uxxxzjMTHH1iUV0NKGiIbOHCgnHbaafLSSy95nOZRA1nTp0+Xa665xkyP2Lxi1NChQ800pZ6q6On28/PzZcyYMXLKKaeYaS89BYo0GKXL8OHDg36+GvrSoJy30JiGs84991zTTk809NQUqtP99Oabb8pnn3120O309aLhtAceeEASElr3gb3uIw136f7wF0TVYJ/uO223Hht9rWrlN5320hMN840ePdrs81DR10Pz/Tp48GD5xS9+Yd4nLWnoTQN5+lo6/fTTzX784IMPPG733XfflZNOOsmECwHAiUa0z5KXTzxE7pq/Rr7dHfg0wO9vKpQle0rlgSMHysDcjLC2EQAAAAAAAIh1TFUJOExlnUt+M29VUKGxIzrlyF+OGUZoDMB+Las0NacVgUJJw2PBtiFaampq5G9/+9tBFY969+5tAkF2odWd9HnefPPNXgM6Vtc8NKaBvmnTpslxxx13UGisJQ3xXHnllSZA5ck333xjppVs/vrU7WqlsECmcdXXit7WW7DJU2DNHw01PfvssybU5cmpp54qd999t9fQWEsasrvsssvM4ml/6TSyM2fODLqdWuXtN7/5jZk+dPLkya2qXqjH8vrrr5df/epXHtum1d0+/vhjCSWtSNfkhBNOkLvuustjaKwlreh3wQUXeK0qptv9+uuvQ9pWAIg17VOTTdXr8wcE9zdhU1mVXPq/JfLG2h0hmUYYAAAAAAAAsCuCY4CDFFXXyrVfLZfZO4sCvs/JPTvIY+MHS0YS03wAODB84StUEkretqdTKlqNVpvSaR+b0/DKFVdc4TeQFIu0KpZWl3riiScOCM/EEg1oadDH17SoLemxvOSSS0w1PE8hrfnz5+//XQNmGjQL5vhrW6ZMmeK1Ulqw+3rWrFmydu1aj+u06pWGl1pTHUyrzmmVMk/ee++9oNupQUSd2jEUdMrQiy++2OO6zz//PCwhAn3Myy+/POj3ulYj7NGjR8iCggBgN4nx8XLjIb3lD0cOkLSEwPvY2nq3PPr9Rrlt3irzvzAAAAAAAACAg9nvE0wAHm0vr5Irvlgqy/YGHrS4aFBXmTamvyTZMOwAoG18hbZ0KrZQ8rY9X+G1aNiwYYPMmDHjoOu10lifPn3EzjQode+990pJSeDTSFmFhotaM4VoXl6eHHXUUT5vo9X3NEjUGhrK0opUniql6WstUHV1dfL22297XDdq1Civwa9A6fSQniqV6Wth7ty5Ek0TJ040U3B6CjyuWbMmpI+l02VeeumlrbqvhvbOPPNMj+vWrVtnjiEAQGRi9w7y9xNGSN/s4M41v9pRJOd98r18uX0vuxEAAAAAAABoIbHlFQDsZ2VRmdw0Z6XsDfBb1nEicsvI3nJO/+CniALgDL4qCelUfqHkbXtWqnDlcrnkueeeM5fNaSBJqwlZke7XYcOGmakRdQpFrXKl1bd0qa2tNcG84uJiWb16taxcuVKWLVt20PNrOT3h//3f/5kpD0MdHgyXrl27mipRrXXEEUeYal7eaGgwKyur1cdHq29phbGWNm7cKEOGDAloOzp1pqdpXTWsdOGFF0pcnP7Vbz29/1lnnSXLly/3WC1Lp26MFm2bhsc8hcSWLl0qAwcODNljafCrLX3fYYcdZu7fsl/T9+LWrVvN+xQAINI3O11ePH6EPP7DJvnPhoKAd4lWHNPKY6f26ig3j+wtmUkMhwEAAAAAAACKkTLA5r4u2Ce//XqVVNTVB3T75Pg4mXb4ADmxe/uwtw1A7PJVAScxMbSnF962Z6UqPP/9739NcKolrUDkaTrDaNEKVlola9y4cSZ4lJSU5PF2GvzSKUK7deu2v5pUYWGhqaj26aefeg2Q6T7QAN2NN94oseAnP/lJm4JTffv29bpO9+3xxx8vbdGvXz+PwTFPrzV3fa1I5a6Drp/1+ccet62vgS5dQhMQ19eITrW4ZcuWA67X6TG1OmFmZqZEi7epL4Op2uaPvlfGjx/f5vemhsM0pOnpeBMcA4AfpSYmyB2H9pUj8nPkwW/WSWmt92B7Sx9sKpRFu4rlzsP6yVH5uexWAAAAAAAAOB7BMcDGPtxcKPcvWicutzug22clJcjDYwfL6I7ZYW8bgNjmq/JUfIint9XKSFYOjm3btk3eeecdj8Ecb6GVaNApBXXavtaGeLR6mk7rOHbsWPnzn//ssYpV07SVuhx55JFidTpVY1vk5OSY/elp6tb+/fu3OTClwT1P9u3bd/CVlbukbvG0A66qqXPLsuUVHrfhb5rNYGn1upbBsfr6elm1apWpphUtGurS8KZO8dmcVvEKleHDh4ckMKuV/zwFx7TyHwDgYCd0ay9DcjPl7oVr5Ic9gU9hXlBZIzfOXmGqj914SC/JSfYcpAcAAAAAAACcILSf7AKwBLfbLa+s2ibTFq4NODTWKS1ZnjtuOKExAG3W1qnvYokGY7TClk4n15wGhi666CKxktGjR4ek8pNO7/fAAw+YIJk3r732ms9woRXk5uZKp06d2rwdDY95oiG9cG27srIyoPuv3VkvnoqwaJBqxIgREkrepn30VB0t0jy97vfu3Ruy7Q8ePDgk28nLy/N4fUWF5/AfAECkS0aK/OWYYfLLwd0k2DNQrT527sffy2db95j/oQEAAAAAAAAnouIYYDMaFHv8+43yxrqdAd+nX3aa/Gn8EMlPt850agCszVsVMKWBoVBOV+ktgBTqKTFb46OPPpI1a9YcdP35559vKh3ZlQaabrvtNrnnnns8hph0WkutOqZV16yqc+fOIdmOt6lIQ7H91NTUNgWJNhZ6fu907do15O8fDeJ5sn379jZvW6uDrVu3zlQ000VDX1VVVea1p5ca4AyWhj11P6anp7e5faGa8lOniG1LUBAAnCoxPk6uHtZTxnTMkWkL10hh1YGBfl+KqmvlzvmrZULnPLllVG/pmuH5by8AAAAAAABgV9H/xBVAyFS76s1A+efbAq+iMbpDlpmeMiuZ7gBA4HyFTnQKyVCGUrxNSRnt4NiuXbvkjTfeOOj6oUOHynHHHSd21717dzP95Ztvvulx/ezZsy0dHMvIyAhrcCwU2/e27ZqamoDuv73I7TU4FmpZWVkery8qKmrV9jQcNmvWLJk7d66ZDjYcdD+GIjgW7tdSy2k2AQCejemUI/+cOFL+8M06+XJHcH9/Zu8skoUf75NfDukuFwzoKskJFOgHAAAAAACAM5AUAWyipKZObp+3UhbvLg34Pid2ay/3HN5fUhgUBxCiSkhNIQdf64OlFYWCbUMkPP/88wcFOpKSkuSyyy4TpzjllFNM1bWSkpKD1i1dutQEc5KTk8WKQhEYitb2A51Oa2+Z50pcc+bMMUsklJeXB10J7IMPPpB333037IGpllPMWvW1BAAIXG5Kkjw0dpDM2Fwoj363UcrrAp86u7reLc8u2yIzNhXKTSN7y7jOnqcQBgAAAAAAAOyEr1ACNlBQUS1XzVoaVGjsZ/06ywNHDiA0BqBVMjMzva4LdBq9QHmbps1bhaNI+N///meCUS1NmTIlZNPWxQIN740ePdprpbj169eLVcXFxcX09gNRaoEZDgOtjqZ2794td911l6nkF0tVtqxwrAEAB/bLp/bqJK9NGimHd8wJetdsLquSm+aslF/PXiHrS0J7XgsAAAAAAABYDcExIMatK66Qy75YKutLAv90+LrhPeXmkb0lng86AbSSr9CWp+pTbeFte77Ca+GkU++9+uqrB13fo0cPM3Wj0xxyyCFe14VrikEEpsYVWGWycHK5XAG/r+6//37ZsmVL2NsEAHCGzukp8uTRQ+S2UX0kPTH44a95BfvkF59+L498t0H2VYemSiUAAAAAAABgNUxVCcSwbwuL5bZ5q6SsNrAPZRPi4uT3Y/rJKT07hr1tAOytffv2XtcVFxeH9LG8bc9XG8LpxRdfPKiqmla2uPzyyyUx0XmnVhqY86awsDCibcGBXJ5nqoyoQKbV1Ns888wzPl8vCQkJ0q9fPxkwYIB069ZNOnbsKDk5OWaaSK18Fx8fbxZPbr31VlPNDADgPPplqbP7dZYJXfLkj9+uN2GwYGgG+811O+WDTYVywYAuct6ArpKRlBC29gIAAAAAAACR5rxPNwGb+GzrHrln4RqprQ+smoh+w/qPRw2SI/Nzw942APanoQ1vdu3aFdLQmLcp63y1IVw0MLZo0aKDrj/++OOlV69eQU3L11xtba3Pik3etqtBNW9hmUjJzs4OeppRREasfK49f/58WbZsmcd1SUlJcsYZZ8jEiRN9vtZ8qa+3QIIOABD16mN/Gj9YZm7ZLY99v1FKauqCun9FnUv+tmKrCZFdMri7nNU3X1ISKOIPAAAAAACA2EdwDIhBb6zdYQa7A52Aqn1qkvxp/BAZlJsR5pYBcIoOHTqYQIenwNOOHTtC9jgFBQVe13Xu3FmsUj3p888/N0s4PP/882bx5KqrrpJjjz1WokkrPrUmEIfwS0uO01ftQdefd955ctJJJ0XkEGg1Pn9mzJjhdUrc3/zmN9K3b982taG8vLxN9wcA2IP+TdLq20fl58qfl2wyVcSCta+mTh7/YaO8unqbXDCwm0zp00lSE2MkqQ0AAAAAAAB4QHAMiCH1OpXT0s3yyurtAd+nZ2aqPDFhiHTNSA1r2wA4i1a50ikK169ff9C6zZs3h+xxNm3a5HVd7969Q/Y4aL2W03Y2p+FCRE+7zDhZ5yF7uWfPHklOThYr0Ckk165d63GdTv/a1tBYXV2d16qFAABnyktJkrvH9JfJvTvJw4vXy7qS4CukFlbVmgDZy6u2mSksz+rbmSksAQAAAAAAEJOoqw/EiBpXvdy9YE1QobHh7TLlb8cNJzQGICz69Onj8XoNjmlYIxTWrVvn8frU1FTp0qVLSB4DbVNSUuJ1XVpaGrs3ijplez7V37lzp1jFqlWrPF6v7+/DDz+8zdu30nMFAFjL6A7Z8o8TD5EbRvSS9FZWDSuqrpWnlm6W0z/8xlQxK6ggrAwAAAAAAIDYQnAMiAHFNbVyw+zl8snWPQHf5+guefL00UMlN4VqLwDCY+jQoV6nJ1yzZk1IHmP58uUerx88eLCpeobo27Jli9d1HTt2jGhbcKA+nTy/R1avXm2ZaUS9TW176KGHhmT7+lwBAPAmMT5eLhjYVd46aZSc0buT+J9g2bOyWpf8c/V2mTJzsdyzYI0s31vGTgcAAAAAAEBM4BNXwOK2l1fJlV8sk8W7SwO+jw54//GoQZLaym9NA0Aghg0bJnFxnj9eW7x4cUgCSTqNnScjRoxo8/YRGj/88IPXdV27dmU3R9GALvEePwCvqqqSpUuXipUr1rVr1y4k21+2bFlItgMAsLf2qcly52H9TAWywzpmt3o7LrdbZm7ZLb/83xK5+LMf5L8bCqSqzhXStgIAAAAAAAChlBjSrQEIqRVFZXLznJWytzrwqiBXDu0hlw7u5jXMAQChkp2dLYMGDZKVK1cetG7evHny85//vE1VwebMmePxeu3fxowZI9GQkZEhr732Wsi3W1hYKDfeeKPHdVdddZUce+yxYkUaQPIWEkxISJB+/fpFvE34UW56vPTLj5e1BfUH7ZYvvvhCRo8eHfXd5XJ5/jA9OTm5zdsuLi6WhQsXtnk7AADnGJibYSp3z9m5T/6ybLOsLa5o9bZW7iuXP3y7Xp5YsklO6tFBTuvVSYbkZfC/OgAAAAAAACyFimOARc3eUSRXz1oWcGgsIU7kzkP7ymVDujMQDSBijj76aI/X79mzRxYtWtTq7dbU1Mj//vc/r9NUMgWiNcycOdNrxSidyjQU4R+0zYTBnr8nooEqK0zjqGFMT4qKitq87Y8++kjq6uravB0AgLPolxQmdMmTV048RO47YoB0z0hp0/Z0Gsvp6wtMFbLzPvleXlm1TXZVVoesvQAAAAAAAEBbEBwDLGj6up1y29yVUuU6uEKIJykJ8fLQ2MFyRp/8sLcNAJobO3as1+DHW2+9JfX1gfVjLX344YdSWup5it6JEydyECxg27Zt8t5773ldP2HChIi2B56NG5gomame17344oumalw0ZWVlebx+xYoVbdrupk2b5P3332/TNgAAzhYfF2cqhb3+k1Fyx+i+0iW9bQEytaG0Up5aullOn/GtXDVrqby1bqfsqaoJSXsBAAAAAACA1mCqSsBC6t1ueWbpZnll9faA75OXkiSPjRssQ9tlhrVtAOBJamqqTJo0Sd55552D1m3dulXeffddmTJlSlA7b/v27R63p/Lz8+XII49s1cHQINvbb78dc9NBtpVWf2vfvn1It6lVxh5++GGprKz0uL5du3YmVIjoS0mKkzPHJMs/Z9d4DFc9+eSTcsstt5ipRUNNXx9paWk+b9O7d2+P1+sUuBs3bvS63peysjJ56qmnqDYGAAiJxPh4mdI3Xyb37igzN++Wl1Ztky1lbQteu0Xku92lZnn0uw0yqmO2HNOlnRzbNU+6ZnhJfAMAAAAAAABhQMUxwCJqXPVy94I1QYXGemWmygvHDSc0BiCqTjvtNMnJyfG4bvr06bJgwYKAt1VcXCyPPvqoVFd7nr7nvPPOk/h4Tl+CofvzT3/6kwnhhMLatWvlrrvukl27dnm9jR6nxES+n2AVJwxPlD4dPb9vvvvuO3nggQdk9+7dIXksnRpyzpw55jWiU5n6o1PPpqQcXMHF7XbLs88+KxUVFUE9vk5xed9995mKeAAAhDpAdlrvTqYCmU5hOSjXc9XdYGl93m8LS+TxHzbKlJmL5YJPvpenl26ShbuKpTrAKuQAAAAAAABAa/GJHmABxTW1cvu8VebbxoEa2T5LHh47SHJSksLaNgDwJz09XS644AJ55plnDlqnU1X++c9/lp/97Gdy6qmn+gx9rVmzxlQJKiws9Lh+5MiRcsQRR3BAgqQBnIULF5pFQzpHHXWU2Y+5ublBbUeDRTqF6Mcffywul8vr7Q477DAZP348x8lCEuLj5JqfpMi0/4hUVBxcJW7VqlXy29/+Vn7605/KiSeeKNnZ2UGHxXRqyUWLFpnX2b59+/a/FvxJSkoyVQS//PLLg9Zt3rxZ7r//frn22mule/fuPrejfc0XX3whb7zxhqmI13z7Wk0t2lNyAgDsI6FxCsufdG8v3+4ukddW75DZO4tCtv21JRVm+ceq7ZISHycjO2TLEZ1y5Ij8XBmQk26m0AQAAAAAAABCheAYEGXby6vk17NXyKYgprqY2L293D2mv6QkUHUHgDVMmDBBli5d6jH8oSGjf/3rXybUccIJJ8jQoUOlY8eOJsyhAY/169fL3Llz5dtvvzUhJ0/y8vLk6quvjsAzsTed/k+Xl19+Wfr06WOmAezVq5cJ5WRlZZlpBTUIWFtbK+Xl5SYApIE+DQXp8fUVGFM9evSQa665JmLPB4HLz4mXm6+9SP7f48+b49uSHu8333zTTBN7yCGHyMCBA6V///6mmmBGRoapCqbhK60ApsvOnTvNVJca7lq3bl3QlcGaO+uss0yVMk+vL32MO+64w4TQDj/8cPO61TbFxcWZ/kMDjT/88IMJrRUUFBx0/3PPPddUPiM4BgAINf1bdFjHHLNsLKmU6et3ygebCqW8zvf5UjCq692yYFexWWTpZslNTpQxnfQxs2V4uyzpl5NugmwAAAAAAABAaxEcA6Jo2d5SuXXuKtlbffAHuN78YmBXuXZ4T75lDMByLr30UhPiWL58ucf1O3bskFdffTXo7WqQ6ZZbbvE6HSaCpwE9DezpEioaQNOqVXq8YE1DBvY1ISydvtRb0EtDZd98841ZIqVTp05y9tlny+uvv+61mlhT1bxgjBs3Tk455ZSApswEAKAtemenyS2j+sivhveUj7bslrfXF8iqfeUh36n7aurk0617zKLSE+NlaF6mjGifZYJkI9plUpUcAAAAAAAAQSE4BkSJDiY/sGit1NR7rq7TktYWu3lUHzmnX+ewtw0AWiM5OVluvfVWeeKJJ+T7778PyU7UsJiGxvr27ctBsXjFucsuu8xUpYK1DRkyRO677z4zLezGjRvFKs444wwTLvVUtbA1tDqZVinUajAAAERKWmKCnNknX87o3UlW7iuXGZsKZeaW3VJSUxeWx6uoq5dFhSVmadIzM1WGtcuUQbkZMiAnQwbmZkh2MsN/AAAAAAAA8IyRIyDC6t1ueX7FVnlhxdaA76NTUj5wxAA5pmu7sLYNANoqNTVVbrvtNjPd3bvvvutxSrxADR8+3AQ/2rWj77MqnZry/PPPl5EjR0a7KQhC165dTXjsww8/NO/Ttkwz6UlmZqaMHTtWjjrqqKDud+WVV5ppbN9++22v09b6o1PgnnnmmWb6S0JjAIBo0b9BQ/IyzXL9iF4yZ2eRCZHNK9gntQF+eay1NpdVmeXDzbv3X9clPUUG5qabENnAnIZAWef0ZP5WAgAAAAAAgOAYEElVdS65b9E6+Wxbw7QSgchLSZLHxg2Woe0yw9o2AAiV+Ph4E9rQaeI0QDZv3rygAmT9+vWTyZMnyxFHHMFBCYFrr71WlixZIitXrjRLaWlpm7aXlJRkgmLHHnusHHrooXzgGKMSExPN++zEE0+UL774wixbtwYeam9JA1/Dhg2T0aNHm0W335q+Y+rUqSY0quExfd0GExjTKmN6/27dugX92AAAhEtyQrwc3629Wcpq62TW9r3yyZY9smBXsbhaGZQO1o6KarPM2l60/zqd5rJPVrqZZrNPVpr0zU6XPtlp0jk9ReKp2AkAAAAAAOAYce7Wfp0fQFB2VVbLbXNXmekqAtUrM1X+NH6IdMtMZW8DiFkaVPruu+9k2bJlJpiye/duqayslPr6ejO1oU5HqRWQBgwYIKNGjZKePXuK05SXl5vqT56MGTNGevfuHbLH0v2/adMm2bJlixQUFMjevXvNUlZWJjU1NWbR00MNiKWlpUlubq506tTJVBfr37+/DB48mCkpLchdvk3qFk/zeZvE0dMkLsN7qGrnzp3mfbp+/XrZvn277Nmzx7w29TWh9PWgVQUzMjIkPz/fvG81pKWvC/091PQ1qn2HBh61bdqXaHU0fW1qOzSspm0YOnSoCTNqX+JJdXW1xwpm2v9QlQwAEC3FNbUyd+c++XL7Xvm6YJ+ZdtIK0hLiG8Nk6dJXLzVQlpUmnTNSJIFAGQAAAAAAgO0QHAMiYEVRmdw2d6UUVgVecWdk+yx5eOwgyUlJCmvbAABA7AtFcAwAAERHtateFu0qNgGyhbuKZUNppeUORUp8nPTMSpNeWQ0VyvRSA2Y9MlMlNSEh2s0DAAAAAABAKwU/hwyAoHy2dY/cu2itGQgO1MTu7eXuMf0lJSGevQ0AAAAAgI3p//7ju+SZpali+aJdJTJ/V0OQbE8QX0ILl+p6t6wprjBLc3Ei0jUjpSFI1mLhi3AAAAAAAADWR8UxIExcbre8sGKrWYJx2ZDucvmQ7hLPFBAAACBAVBwDAMCedLrl9SWVsmBXsXxTWCxL95ZKUXWdxIK8lMSDAmX6e+f0FMY8AAAAAAAALIKKY0AYFNfUyj0L1sq8gn0B3yc5Pk7uGtNfTurRgWMCAAAAAAAkLi5O+uWkm+W8AV1MkGxbebUs2VsqS/aUytK9ZbK2uFxcbuvtLA24FVWXyne7Sw+qsNYrM9VMddkw9WW69MpKlR6ZaVReBwAAAAAAiDAqjgEhtrKoTO74erXsqKgO+D7tU5PkobGDZHi7LI4HAAAImrt6r7jWv+HzNgl9fyZxKe3YuwAA2ExlnUuWF5WZENmqonJZXVwuW8qqJNbEe5r2MrshVJaTnBTt5gEAAAAAANgSwTEghN7buEseWrxeauoD/6rvwJx0eWTcYMlPT+FYAAAAAACANiuvdZlKZKuLK2T1vnKzrCupkNogxiusJC8lSXpnpUpvU51Mq5RpqCxNOqUlM+0lAAAAAABAGxAcA0KgxlUvj36/Qd7ZsCuo+x3XtZ1MO7y/pCUmcBwAAAAAAEDY1NXXy+ayKtlQUikbSipkQ2nD5abSKqlzx2agLFWnvWysTtY3O13656TLgJx0EyjTaT4BAAAAAADgG8ExoI12VlTLb79eJcuLyoO63yWDuslVw3rwzVgAAAAAABDVQNnWsmpZX1phQmXrSypkY0mlbCqrjNkKZVlJCSZE1j8no/Ey3QTL0vniHgAAAAAAwAEIjgFt8HXBPrl7wRoprqkL+D7J8XHy20P7yU97dWTfAwAAAAAAS6qrd8u28irZWFopm0orzaUGyvSyvM4lsUbrj3XLSN1flUwvB+dlSj7VyQAAAAAAgIMRHANaoba+Xv66bIu8snp7UPfrkp4i/3fUQBmSl8l+BwAAAAAAMcftdsvuqloTJtvQFCrTQFlZpRRW1kisyU1OlMF5GTI4N3P/Zed0proEAAAAAADOQHAMCNLWsipTZWxZUVlQ9zsqP0fuO3yA5KQksc8BAAAAAIDtlNXWyebShiplDUuFbCqtki1lVeJyx860lzkaJsvNkGHtMmV4uywZ3j5TcpIZzwEAAAAAAPZDcAwI4hu1M7fslocWb5CKIKdkuHRwN7l8aA9JiNOJEQAAAAAAAJyjrr5etpZVmyDZRhMs00CZBsuqgh5jiZaemakNITINk7XPkn7Z6ZIYzzgPAAAAAACIbQTHgAAUVdfKH79dL19s3xvU/spMSpBpY/rL0V3bsZ8BAAAAAABafEmvsKrGTHV5wNSXpZVmOkwrS02INyGy0R2yZVSHbFOVLDUhIdrNAgAAAAAACArBMcCPL7fvlQe/XW/CY8Hon5MufzxqoPTITGMfAwAAAAAABDnt5camIFlJ09SXlbKtXKe9tN6uTIyLk6GNQbJDO2TLiPZZkpFEkAwAAAAAAFgbwTHAi+LqWnn8h00yY3Nh0Pvo5B4d5LeH9pXURAYIAQAAAAAAQqW2vl62lFXtr0ymobK1JRXmss5tnURZQpzI4NxMObxTjlkOaZ8lyQnx0W4WAAAAAADAAQiOAR6mSfhk6x557PsNUlRdF9T+SYmPk1+P7C1T+uRLXFwc+xYAAAAAACBCgTINk60trvhxKamQwsoaS+z/lIR4GdU+y4TIjsjPlQE56RLP2BEAAAAAAIgygmNAMzsrquXhxRtk9s6ioPdL3+w0eeCIgdIvJ519CgAAAAAAYJGK8hogawqTrSkul3XFFVJTH93qZDnJiSZENjY/V8Z2zpX2qclRbQ8AAAAAAHAmgmOAiNS46uW1NdvlxZXbpMpVH/Q+OatPvtx4SC+mpgQAAAAAALC4uvp6WV9SKSv3lcvKojJzuXZfuVRHMUw2ODdDxnXOlXGd82Rou0xJoBoZAAAAAACIAIJjcLzZO4rkT99vlK3lVUHvi9zkRPntoX3luG7tHb8fAQBA9LjLt0nd4mk+b5M4eprEZXSLWJsAAABiSV29WzaUVsjKonJZUVQmS/eWydricnG5o1ONTCuRaZDsqPxcyUlJinwjAAAAAACAIxAcg2Pp4N9TSzbLvIJ9rbr/0V3yTGiMqQQAAEC0ERwDAAAIvco61/4Q2dK9pbJkT5nsra6N6K6OE5Fh7TJNJTINkg3KzZB4qpEBAAAAAIAQITgGx9lZUS3PLd8iMzYVSmu+NJqemCC3jOwtp/bqKHEM1AEAAAsgOAYAABCBcy63W3ZUVMsPe0pl8e4S+W53qWwsrYzorm+fmiTjO+fJhM55cnh+jhmnAgAAAAAAaC2CY3CM3ZU18uqa7fLWup1SU9+6eQZ0moDfjO4rXTJSQt4+AACA1iI4BgAAEB17qmrkew2SFZaYMNna4opWfVGxNZLi4+TQDtkyoUueWbpmpEbokQEAAAAAgF0QHIPtFVRUyz9Xb5d3NxRIdSsDY7nJiXLzyN7ykx4dqDIGAAAsh+AYAACANZTU1Ml3u0tk4a5iWbCrOKIVyfpkpZkA2fgueTKiXZYkxutElwAAAAAAAN4RHINtrS+pkH+v2SEzNhdKbSsDY+rknh3kpkN6S25KUkjbBwAAECoExwAAAKxpV2W1LNpVIgt27TNhst1VtRF53OykBDmqc66Z0lIvc5IZ1wIAAAAAAAcjOAZbqXe75euCfSYwNn9XcZu21Tc7TW4Z2UfGdMoJWfsAAADCgeAYAACA9bndbtlQWinzC4pl3s4i+XZ3SZu+7BioeBE5pEOWCZFpNTKtTBYXRzUyAAAAAABAcAw2UVhZIx9sKpT3Nu6SreVVbdpWRmKCXDm0h5zdL18S43VoDQAAwNoIjgEAAMSeyjqXLNpVLHN37pO5BUWys6ImIo/bJT3FTGmpQbLRHbMlJYHxLwAAAAAAnIqKY4hZVXUumVuwT2ZsKpS5O4vE1cYvaOoQ2eTeneSqYT2kfWpyqJoJAAAQdgTHAAAA7FGNzITIdhbJd7tLxeUOfzWy1IR4ObRjthzZKVeOyM+hGhkAAAAAAA5DcAwxpcrlkvk7i+XTbbvlq+1FUumqD8l2j+mSJ78a3lP6ZKeHZHsAAACRRHAMAADAXspq62RhUzWynUWyu6o2Io/bMS1ZjuyUI0fk58oRnXIkLyUpIo8LAAAAAACig+AYLG97edX+QbJFhSVSHaKwmDqkfZZcN7ynjOyQHbJtAgAARBrBMQAAAHtXI1tdXCGzdxTJnB1FsqyoLGKPPSg3Qw7rmC2jOmTLqPZZkkOQDAAAAAAAWyE4BsvZUV4ti3eX7F+2lFWF/DEO7ZAtlw3pbga+4uLiQr59AACASCI4BgAA4Bx7qmpk3s59Mntnkcwv2CcVdaH7kqU//bPTZVSHLBndMVtGd8iW9qnJEXtsAAAAAAAQegTHEDUut1sKKqplbXGFrNxXLiuLyszlnjCW3tcS+5cO7m4GtwAAAOyC4BgAAIAz1bjq5bvdJSZEphXJtpVXR/Txe2Smyoh2WTI0L0MG52XKwNwMSUmIj2gbAAAAAABA6xEcQ9jU1ddLcU2dCYLtqqyRnRXVUlBZLdvLq2VjaaVsKa2U6np32I9AUnyc/KRHB/l5/y5m8AoAAMBuCI4BAABAp7TcVFolczREtrNIvt9dIq7wD70dICEuTvrnpMuQvAwZmpcpQ/IypU92miTFEyYDAAAAAMCKCI6h1ZbsKTXfZNSKYVUul1S56qXaVS8VdS7ZV10n5XWuqO7d9qlJcmaffJnaN5+y+QAAwNYIjgEAAKCl0po6+bqgYUpLndpSv+AZDRom08pkGiDrk5UmfbLTzc89M9OoTgYAAAAAQJQlRrsBiM1vL764cpv8dfkWsZqEOJFxnfPk9N6dZFznXEnk24wAAAAAAABwoKzkRJnUo4NZXG63LNtbZr4EOke/CFpSEbF26GPr7AO6/K/Z9VqDrFtmqgmVdU5Lkc4ZKdI5LVk6p6eYpUNasgmdAQAAAACA8CE4hqDNK9hnudDY4NwMmdi9vZzSs6MZVAIAAAAAAADQQANYh7TPMsuvhveUnRXVsqBgn8zfVSwLdhVLSRSqkdWLyJayKrN4a3OntGTpkJokuSlJkp2cKDlmSTKXuSkNv2cmJUpqQrypXqaL/pycEC/xbQyd6ZdndarPOne91NW7xVXvltp6t9S59bK+4ed6t9Q0+9lc73JLrbvhulpX42XTusZL3YbbLaIzidbrD+bxdJ80XK+0/fol2YR4vWy2NP6eEh/X8JwTE8xz3r8kJkhKfLykJcab8GBaQrzEEcADAAAAAHhBcAxBm76uwBJ7bUBOugmLndi9vfTITIt2cwAAAAAAAICYoBW9Tu+TbxatCLZ6X7nMLyiW+bv2yQ+7S02wKdq0XTsqqs3SGsmNwaqkeA1ONVQ40x80TmaWOL1sCJfVNYa5NPxVtz8cFv19EAoaPtNwXVZSQuNlomQmJ5jL3OREyUtpCOa1M5c//q77DgAAAABgfwTHELSimtqo7DX9dtzhnXLMVJQ6DWV+ekpU2gEAAKyvqqpKVq1aJRs2bDDL5s2bpbKyUurq6iQxMVHS0tKkZ8+e0qdPH7MMGjRIUlNTo91sAAAAIOK0etWQvEyzXDK4m1TUuWRxYYl8u7tEFu8ukZVFZabyVqypMdXAXBpBEyfTY1dcU2cWkcBDeOmJCabaW8e0ZOmYmtxw2bSkJptqcO1TkyQxnoAZAAAAAMQygmMImn77LFJBMS2fP7pjtozqkC3D8jJNmXkAAABvNCD2ySefyOzZs6W62vuHIiUlJVJQUCALFy40v6ekpMiECRNk0qRJJlAGAAAAOJUGhsZ3yTOL0iDZkj2lJkT23e4SWba3zISyYG963DeX6eJ5KlGl9dq0QpmGyTo1LlrNTpcujZcaLmvrtKEAAAAAgPCJc7stUHccMeXbwmK55svlId1mUnyc9MtOl8F5GTI4N9Nc6lSUfGMNAAAEYsuWLfLyyy/L8uVtP0cZOnSoXHzxxdKjR4+Y2fnu8m1St3iaz9skjp4mcRndItYmAAAA2FO1q16W7y2T7/eUyoqiMrMUVNZEu1mwKB33zfcQKGv6OT89mTFgAAAAAIgigmNolX+s2ibPLtscVJn6pkGCTo2DAn2y0qRXVpr0zkqTrhkpDBAAAICguVwuee+99+Ttt98201CGik5nedZZZ8nkyZMlISHB8keG4BgAAACiaU9VjawoKpflRWUmVKZhsn1makTAN61FphXLDg6V/Rg2S0u0/v9kAAAAABCrCI6h1VbtK5f5BftkY2mlJMbFSUpCvKQmxktqQoJkJydKTnKi5OplSpJ0SE0yZcspSw4AAEKlqKhIHnvsMVm3bl3Ydmq/fv3k5ptvlry8hml6rIrgGAAAAKxEJ7nQKmTrSypkQ0mlbCitkI0llbK+pFLK61zRbh5ijI4za4CsqXJZvgmUJUt+GtNhAgAAAEBbERwDAABAzCksLJQHH3xQCgoKwv5Y+fn5cuedd0rHjh3FqgiOAQAAIFYCZburamVDSYUJkW0rr5KdFdUNS2WNlFClDK2gX2rupKGyjBTpnNYw/aWpVpaWIp3Sk6VDarJkJSVIXJzWNwMAAAAANEdwDAAAADFXaey+++6LSGiseXjs7rvvtmzlMYJjAAAAsIOKOpcJkRVUVMuOihrZVVktxdV1UlyjS23jZZ0UV9dKdb1brB5mSopvWBLj4yU5IU4S4+Ibf48zMzNojEmzTPESZy4bfo/bH7JzmUXEVe+WOrdb6huvq6t3S019vVTV1UuVq16svSesISU+TtqnJkuHNA2S6QwZLX42S5KZSYOAWeTVN76uVdPr2d30U7MXuL53EvS9QwgQAAAACBmCYwAAAIgZLpdLpk2bFtbpKX1NW6mPnZCQIFZDcAwAAABOU1XnMiGyyrp6qa6vl2qXBqlc5rLpd11q693idjeEUBouGxf9pZEGUTTQlRAfb4IpGvoyl40/N4W/ml+v1yU33j4pviEQ1nTZFAyLBH0eNfVuqXK5TJBMn3Olq14qal1SWlsnZc0uy2rrzM+lNbrvaqWouk72VTcE8gifNdDjl5ucKDkpSQ2XyUmSm5JoAmW5yUmSk6KXiZKbkmSm0NT16Ynxtg0y6etLQ4v6Pmt6jWlY0bzfGt9z5rLZ7/vXuQK7T7XeJ8ggqL5nm96HTe9Lff+lJMRLakK8pCXqZYKkJsZLWkJC4+96fcL+S70uPTFBMpMSJTMpQbIaL3XR9zsAAADgFInRbgAAAAAQqPfeey8qoTGlj/v+++/LGWecEZXHBwAAAPCjVA2AJFrvSx2RpoGllARd4iUnuXXb0CpmWtltX02t7K2qNZd7qmpld2WN7KqqkcLKHxcNpdmZBg0Lq2rNEiiNGGUkJTQsiXqZ2HjZ8LuGlPT46JIcH2eCS02/m+sS4k0Qav9iqmqJCR82XafBR81WNYUeGy5FtN6cXmoFulpXQyU6fQ4Nocl6Eyqsdell858b1ptQlwly1R/0+/5Ql8tlqt5ZjanG59LnEZ7t6zHS6U2bQmUHhMuSG37X9RmNl3p9RrPwmd7frmFCAAAA2A/BMQAAAMSELVu2yPTp06PaBn38Qw89VHr06BHVdgAAAABAqGgwqV1qkln6Znu/nQaWyutcPwbJTKisVgorq2VXZY2ZZlSXktowpXksSqN0paaym7Oet501BeeCCRA2p8E/DZVlmopmDUEzDZY1D6E1hQwzPVyvP9u5kh0AAACsheAYAAAAYsLLL79spqqMprq6OtOOu+66K6rtAAAAAIBI0xBLQ7glUfpkp3u9XXmtywTIdjQGyVpeajUzwM60SltJTZ1ZWqupkt0BobPExnBZY8Asveky0ft1ehmpqXMBAAAQmwiOAQAAwPI2b94sy5cvFyvQdmh7evbsGe2mAAAAAIDlaFilX066WTzRaRELmoXJmgJlDUuN7KqstuT0iECsVrLT6mUHBswSJT1Jr2sIpTUPmTWfZrXldUzBCQCwirr6eqmsa5iiW6fnrjOXbql1N/u5cQrvumY/63TXZrpvt9v8re2UmixD22VKdjKxGTgb7wAAAABY3ieffCJWa89ll10mlhGfJJLexf9tAAAAACDKUhLipWdWmlk80Q/3dCrMnZXVjQGzmobLxt93VNRIRR3TQgKBqqirN4tI26r9aRW09BZhskBCZ3qftIQESU6IM+9/s8Q3XCYnxFuuIppOy1vndkuNqyFoUKOLy20uNXRQ42q4rrb5deZ3vb7pPu4Df3c1u1292wRo6xoDDE3hBXPZFGZo/nOzdSo+To9FnOhu033X9LteamXIhMZLPV66XqcjToz/8XL/z96u15/33y9eEuNEEvSy6frGy/0/t7y+xXYO2m6Ly6YpWd2Nz1UvNTy8/1Ka75eGS1fzpV6kzl1vbutq3Kd6/Jp+Nr83+7nhevF7m7qWt69vfAwvt2m5PXfj/m/al2aJb3ZMGveBHrem9eY90ey9kRLfeF3j+6Zp3Y/r4w94X+n6pPgf9ylgBfreqnK5zLmbBr0qGy/N764fr9O/Ux5vZ27T/Dq9X0NfGirab/5qeC+5YEAX3j9wrDi3/uUFAAAALKqqqkquueYaqa6uFqtISUmRv/zlL5KamhrtpgAAAACA45TV1u2vUPZjqKzGXFdQWW2CZ1QtA2JDcnzc/mBMQxBGAzAaqGkI05hgVLPwTfPfm/+8P4Sl4SL58ecDrm92nYYZqk2Qq1kwrDHsxQenkaMBN93f7PPQ7c/9AU1/S2MQLbXZdc1/9rQkmTDhwQHA5pf6fkRs0D5R+z7TH7rqzVLZGOBquGy6zmV+1kv9velnvTS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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1223 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "pc_mu = az.plot_dist(\n", + " idata_partial,\n", + " var_names=[\"mu\"],\n", + " visuals={\"title\": {\"text\": r\"Population mean $\\mu$\"}},\n", + ")\n", + "az.add_lines(\n", + " pc_mu,\n", + " values=TRUE_MU,\n", + " visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_MU:.2f}\"}},\n", + ")\n", + "pc_mu.get_viz(\"plot\").legend()\n", + "\n", + "pc_tau = az.plot_dist(\n", + " idata_partial,\n", + " var_names=[\"tau\"],\n", + " visuals={\"title\": {\"text\": r\"Between-market SD $\\tau$\"}},\n", + ")\n", + "az.add_lines(\n", + " pc_tau,\n", + " values=TRUE_TAU,\n", + " visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_TAU:.2f}\"}},\n", + ")\n", + "pc_tau.get_viz(\"plot\").legend();" + ] + }, + { + "cell_type": "markdown", + "id": "ef1c249d", + "metadata": {}, + "source": [ + "The posterior of $\\tau$ is concentrated well away from zero, which is itself the result of substantive interest: the eight markets disagree about the size of the treatment effect in a way the data demand be respected. The conversion-rate version tells the same story, as we confirm next.\n", + "\n", + "## The same machinery on a binary outcome\n", + "\n", + "The conversion-rate version repeats the structure on the log-odds scale. Each market $k$ has its own baseline rate and its own treatment log-odds effect $\\theta_k$; the population sits a level above ({cite:p}`carpenter2016hierarchical`)." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "a8ee0c5e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:34.140359Z", + "iopub.status.busy": "2026-06-01T17:59:34.140263Z", + "iopub.status.idle": "2026-06-01T17:59:34.143762Z", + "shell.execute_reply": "2026-06-01T17:59:34.143250Z" + } + }, + "outputs": [], + "source": [ + "TRUE_MU_LOGIT = 0.20\n", + "TRUE_TAU_LOGIT = 0.25\n", + "# Dedicated generator for the binary arm (as with `meta_rng`): keeps this section\n", + "# reproducible on its own and unaffected by the Gaussian arm's draws.\n", + "bern_rng = np.random.default_rng(2024)\n", + "BASELINE_RATES = bern_rng.beta(20, 180, size=K)\n", + "\n", + "\n", + "def simulate_meta_dataset_bernoulli(\n", + " K, N_per_market, baseline_rates, true_mu_logit, true_tau_logit, rng\n", + "):\n", + " from scipy.special import expit, logit\n", + "\n", + " theta = rng.normal(true_mu_logit, true_tau_logit, size=K)\n", + " n_A = np.zeros(K, dtype=int)\n", + " n_B = np.zeros(K, dtype=int)\n", + " for k in range(K):\n", + " p_A_k = baseline_rates[k]\n", + " p_B_k = expit(logit(p_A_k) + theta[k])\n", + " n_A[k] = rng.binomial(int(N_per_market[k]), p_A_k)\n", + " n_B[k] = rng.binomial(int(N_per_market[k]), p_B_k)\n", + " return theta, n_A, n_B\n", + "\n", + "\n", + "true_theta_bern, n_A_obs, n_B_obs = simulate_meta_dataset_bernoulli(\n", + " K, N_PER_MARKET, BASELINE_RATES, TRUE_MU_LOGIT, TRUE_TAU_LOGIT, bern_rng\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "e4d6eb38", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:34.145276Z", + "iopub.status.busy": "2026-06-01T17:59:34.145189Z", + "iopub.status.idle": "2026-06-01T17:59:37.211234Z", + "shell.execute_reply": "2026-06-01T17:59:37.210473Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "NUTS[nutpie]: [mu, tau, theta_offset, baseline_logit]\n" + ] + } + ], + "source": [ + "with pm.Model(coords=coords) as partial_bern_model:\n", + " mu_logit = pm.Normal(\"mu\", mu=0.0, sigma=0.5)\n", + " tau_logit = pm.HalfNormal(\"tau\", sigma=0.5)\n", + " theta_offset = pm.Normal(\"theta_offset\", mu=0.0, sigma=1.0, dims=\"market\")\n", + " theta = pm.Deterministic(\"theta\", mu_logit + tau_logit * theta_offset, dims=\"market\")\n", + " baseline_logit = pm.Normal(\"baseline_logit\", mu=-2.0, sigma=1.0, dims=\"market\")\n", + " p_A = pm.Deterministic(\"p_A\", pm.math.invlogit(baseline_logit), dims=\"market\")\n", + " p_B = pm.Deterministic(\"p_B\", pm.math.invlogit(baseline_logit + theta), dims=\"market\")\n", + " pm.Binomial(\"obs_A\", n=N_PER_MARKET, p=p_A, observed=n_A_obs, dims=\"market\")\n", + " pm.Binomial(\"obs_B\", n=N_PER_MARKET, p=p_B, observed=n_B_obs, dims=\"market\")\n", + "\n", + "with partial_bern_model:\n", + " idata_partial_bern = pm.sample(\n", + " draws=2000,\n", + " tune=2000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "a5796f5c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:37.212716Z", + "iopub.status.busy": "2026-06-01T17:59:37.212623Z", + "iopub.status.idle": "2026-06-01T17:59:37.407819Z", + "shell.execute_reply": "2026-06-01T17:59:37.407400Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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LTJs2zbz30v3UjIp676X7o/fauk9NmjQx90ev2/Xq1Yt0sz3BK+eg3u+feN7Tc1CDr0/c/584B6tXr26eg/q8qeegm/cnWF7df92/xYsXm+f2ifdi+myi57c+7+s7MO0L0GfEtLQ081jov1oivWLFimb/g05VqlT5/z4hPS56jxlu//jHP8yMusHS/hXd3zJlyoiX2wfAQwwAsKlmzZqaf9+V09ixY4Pal+3btxtff/218eijjxo9evQwGjZsaCQlJYWsfWXKlDEuvvhi45133jH27t0blnPRTnt79+7tSBt0PVbboOdbLGjXrp2l/X/llVdc/ffsxPeTlZVlxMfH22pHo0aNjHAqLCw0fv31V+Puu+826tevb/vaEBcXZ3To0MEYPny4kZmZ6elrdufOnS2v78MPP7R1rAYNGhT0Ni+99FJb21y4cKHl/a1cubLh9fPbKbGwz4899pitNvuyZcsW815Jz7lg16vX93POOceYOHGi4SV27n18fR9HjhwxRo0aZdSuXTuo9aWkpBhXXHGFsWjRIsv7tGnTJqNfv35GqVKlgt6f5s2bG2+99ZaRm5trhIMX7vFD+Tev+6DHrkqVKgGvT6+fkWpvoNf5m266yZHr+6uvvmq7PdH4+xNt95RuMXToUMv7df311xuxxA3PnicUFBQYI0eONNLT0x09FwcOHGhEK30uT0hIiPjfczBTq1atjGjhtj6hSP8uB3NP98wzzxidOnVy9PzUe8N7773XfB53ix9//NG8n7Syn02bNjVef/1149ixY0Wu/9lnnzXKli1redJnQi/y0jn4008/WT4HW7RoYYwePdr8LQnVdWfjxo3sv8O2bdtmjBgxwuyLTU5Odvx3WvshtC/gqquuMp5++mlj8uTJxuHDh41waN26taU267WU9gHwCgLHANgWCx3Gffr0MapWrRrRtiYmJhrXXHONMWfOnJCelXbaSOCYM9auXWv5O9CXtF7ovNdOKDvt0Bdt4aAPt/oizokXe0VN+mL72muvNRYvXuzJa/YTTzxheX233XabrWN12mmnBb1NPXf1pa9VL774omteJkbj+W1XLO1zKF7+HDhwwLjvvvsc60A866yzjNWrVxteEIrAsQ8++MCoWLGi7aCSXr16md9toDRYbcCAAY4EXtWtW9f4+eefjVDx0j1+KP7mNZBCX4wVK1Ys6PW5OXBMf6dvvvlm29+tvkQbN26c4dXfn2i7p3QL/duwul86qCGWuOXZ888WLFhg1KhRw7FzUQPRwhVA7LRZs2ZF/G852Emv7dHAjX1Cbg8c0/uoyy67zLyvCvV51L59e+OTTz6x9Vxvhw7ssDOA7s9TpUqVjPfffz8qg3bcxkvnoN4rdunSxZF90Wexjz76KKrOQS/uv97/XH755bYHcluZdJvNmjUz+vbta957hMqQIUMstU+DRMPB7e0D4A3xkc54BgBuoOVWNNVupMvlfPzxx9KuXTu58sorZcuWLRFtD0JHS2FYUbt2balZs6Z4QWKivWraJUuWlFDSVNwjR46UunXryv333y9r164N2bby8vLko48+klatWsmtt94qu3fvFi8555xzLC+raeSt0tKDWprQSgp7LRFnlZafiMSx8vr57cV9DpaWENbSAs8//7x5vJyg57uW5vjyyy8dWZ9XaFkMLWVw/fXXm6VB7dAxBe+//755Ps6ZM8fv/L///ru0aNFCXn75ZfNctkvLfHTr1k2GDh1qtsVp3ONbp89GZ5xxhjz44INm2dFYoeeZlvp7++23ba1HS8BOmDBBbrjhBlvr4ffHe06UdQ33sgiM/h7qb51Tz936nb3++utRefidLt0ZDnpfGQ3oEwruXlFLvmpf6RdffGH2nYaaluW+6qqrpE2bNjJ16lQJ5z3Kc889J23btnVsu1pquFevXnLBBRfIgQMHHFmn13jtHHzhhRfMc3DKlCmOPVNce+21ctFFF7n+HPTi/h85ckRuv/12s8Tm559/LoWFhWFvg25z2bJlMmbMGLPfKVQ6d+5sablZs2aZfb2h5vb2AfAGAscAwIU+++wzadasmfkvYs+kSZMsLXfWWWeJFxQUFNh+4ClXrpyEyqJFi8xOhHvvvVf27Nkj4XyQHj16tHltsHoORSM91iVKlLC07MqVKy1/R/rgbTU4xmrAmnZS2Ql2cyJwzIvntxf3Odjz8qGHHjJfNuiLB6cdO3bM7IjXYDr4pwML9KXF119/7ejh2rRpk3kNmT59epHzfPjhh+Y8GzdudPwcGzJkiNx9990S66LlHn/16tXSqVMnmTlzpsQSPdf0xYhee+1IS0uTb775Ri677DJb6+H3x5vsvJD7448/HG0LTq569epm4LHVZ5C/e+2118xn3GhD4Fjo0CcU2G+2/u2ccsopZjBDpP4Gzj77bBkwYEDIA3dzc3PNQKFBgwY5MjjjZOecBoZoHwkC47VzUM+76667Tu677z7HBor92ffff2+eg3YGWoaSF/d/3bp10r59e3nzzTdDMojLbXRfU1JSLN27//TTT+L19gHwBgLHAMCldMSHZh575plnIt0UOEgf9H29lPXFK4FjOrLO7gg+zYYSCq+++qr5wn7JkiUSKRrYcuGFF8rgwYPFK9nnzjzzTMvLW/17sxPAZTVr2IoVK2Tv3r2Wlq1fv775kssOL57fXtznYGiHqY6O1XuRUHYkakdX7969bf3deSVoTEehalBPKGhWKQ0Q1GCWv3vllVfMDGeh6EQ/QbOYaZaFWOf2e/wNGzaYv7ubN2+WWKLXsP79+8tbb71laz0aSKIj4bt3725rPfz+eJcGHlo1d+5cmTx5sqPtQdH31pr5wgk7duyw/EwSSdEWOJaQkGAGeLgdfUKBZf/We6U77rjDHGQS6fsHvQ/u0KGDbN26NSTbyMnJkfPPP18+/fRTCSUd/KHPEm4KXHErr52D+ox38cUXm5VQwnEOLl68WNzEi/uvA8e6dOniqWDS1NRUs//PilBmQouW9gHwBgLHAMDlNMvHSy+9FOlmwCGa6lo7hazwSuCY3dJByuqDlq+gBs2Ecuedd4Zk9KeVjqMnn3xS+vbtG5Wj18OZSSsSgWNWl41UmUovnt9e3OdgaQCvdpaPHz8+bNu75pprXFm+wS3lKTVQxelsXycLHtNsB39+QfLJJ5/IXXfdJeHwyCOPmAHkXuDGe/yDBw+aZVSipYRuMPTF3xtvvGFrHWXLljWDduwEtPP7g/Lly9s6CPpbaaWcOoKn90EazOEEt2ea/Du9P4624JJGjRrZCswMF/qEfNPs89r3FakMT0VZunSpmQ3G6YAPffa7+uqrHSuL54/e42kGKw0awcl57RzUvogbb7wxbIEnOlhS+6/Wrl0rbuDF/dcMh5deeqlkZmaK11h9t6LnRziysrm9fQBiH4FjABAFNE2ylk1D9LOaOrhSpUpSu3ZtiXX6Mm7cuHG21lGsWDHHOvhP6Nevn+te7p4IstOSS7HOTlCUlSAuHW1opxSQlvNbs2ZN0MtFqkylF89vL+5zsG644QazFFs4bd++Xf71r3+FdZvRQstmrFq1Kizb0uvXww8/bP5vDU7QcyFcnZAaQKhZoeyUcosmbrvH79OnT0yOOtegsddff93WOvRefOrUqdKmTRtb6+H3B7Vq1bKdqVSzjmgAfKiDiSEyYsQIiYuLs30onC4xHY4AhVBmGQ2FU089VaIBfUK+s7Ked955ZnZFN9Lsgd26dbP0rF8UvecO9/VBg8c0u5IOGMFfefEcfPrpp+Wjjz6ScAfn9ejRwxy0Emle3H/NfH2yLONe0KlTJ8vXzXAcM7e3D0DsI3AMAKKAvkTr1atX1HXc4X9ZDUYJVelFN/nggw/kH//4h+1sOz179pT09HTH2vXggw/aLmsUSlpC5YknnpBY1qxZM6lQoYKlZXU0pmbqCYZ2EmppAjusZA+zGjimL7M0xbwVXjy/vbjPVoS6TENRNCOQlmTEX3333Xdh/x60hKtmtgn3/aeWxgp1qR63cNM9/rvvvht1gQ2BGDBggLz22mu21lGzZk0zg6nej9jB7w+UE6X09NqhAfD16tUz7wFHjRplljwn04DzmjRpYr6kt0uzeoSqxFgoLFy4UKJNtASO0Sd0ctoPpP1B8+bNEzfTl/N6TdCsQXZNnDhRhg8fLpEKDtXyh/D2OThz5kwZMmSIRMLq1avN0u2R5MX9379/vxkU71V23q+EIzO629sHIPYROAYAUWL9+vU81Ec57eDXl7BWxFrgmJa+0E4O7TTVFx3ayasvTu2OeExNTZXHHnvMsXZ+8cUX8uyzz4rb6T5rtrZYpYFRWk7BauffjBkzwpb5y+o6dMSojh61+gJSy2cFy4vntxf3OdqceBmOyNJAJh3tGqkSGs8//7x4hVvu8QcOHCixRkus2j22DRo0MIPGNEDHDn5/cELTpk2lZMmSjhwQzc6omfDuuecec716P3jhhRea9xHffvutmckT9t18882OHEY3ZZgMZJ81ENHupNc+Xxo3buzIdnSKht8x+oSKpsEbv/76q0SDzZs3S+/evW0F62pmq1tvvTWiAb9arg7ePQf1eU9LNOp1KVIiuW2v7r8O2vZytsEqVapImTJlLC0bjqBSt7cPQOxLjHQDACAapKSkSMuWLaV169bmywOdtFyJZsApXry4+XlSUpJkZWWZ04EDB8yXQOvWrTODB/TlrxPph5977jlz1LxuC9FHR/Tl5ORYWrZ58+YSLZ0XTpTysEpLnNWoUcORdemI8Jtuusn2evR4aKr7Cy64wHwJrw+BpUuXNjsKNVBIM1N99tln5ksfq7SzSEuJLVu2zFx3LNJSjOPHj7e0rF6Hgylf6kTgWLAZx6xkKLNTptKL57cX9zlaaWemBvglJCREuimeFskOZc38qNlzNNNLKHGP/1+HDh2SWKIBBC+//LKtdejADS0pVrFiRVvr4fcHf5aYmGjel1q9r/VF+yE0g41OJ1SuXNkssXpiat++vaUBB16m9336e2E3yGLOnDlmdmwv8Ze5rFWrVuIlXugTspr1R8vFRRO9zmpGUy2HbcXQoUNl27ZtjrcL1njxHBw5cqSjJS+jjVf3319Aty/x8fHStWtXM+OdviPT/vdy5cpJWlqa+ZlWbtB+sV27dpmDF/T4ama1+fPnmwPp3RKsqr+nVvpgwxWY5fb2AYhxBgDYVLNmTR3e4spp7NixAe1D1apV/2fZevXqGQ888IAxZcoUIzc319YxysvLM9ui67S7T5988omtttjZdu/evQ0n6HqstkHPt2j15ptvWt7vBQsWGF7/e/Y3/eMf/zAKCwsdOxZXXnml7TZ169bNWLZsWUDb+/nnn41atWrZ2t5dd90Vs9fsDRs2WF5vp06dAv7e8/PzjRIlSjiyPxs3bgx4u9ddd53l7UycONEIVqye3+zzfz322GMh+TstWbKk0adPH+P99983fv31V2PRokXGpEmTjOeee85o0qSJY9vR+69YYufep6gpOTnZuOyyy4x3333X/C4WL15sTJ482fwumjVrFpLv/89Thw4djBdffNH8/vU8mDZtmvHKK68Y7dq1c2T9Q4YMsX3cvXSPH6q/eavT3XffHdL2+jJw4EDb7W/fvr2xf/9+wwmx+psbrfeUbqDXzUgenwYNGhg333yz8fHHHxt79uyJ2HGwew6Fs2+gY8eOjjyves1FF13k85iMGDHC8BI39wmF8nfZl4KCAqN169aOXd9atWplPPXUU8bs2bONLVu2GDk5Ocbu3bvN++S3337bOO+884zExERHtlW6dGlj3759Qe/ztm3bjJSUFMf2uUqVKubvtt5L/vbbb+Z9+Q8//GCeb/o3qM8MTm3Lan+Hm3nxHDx06JD5XO/UPlevXt249957jfHjx//lHBw9erT52+fk+e7EOejV/ddz0WpbTj31VGPFihWGVcePHzdmzJhhPPnkk8ZZZ51lJCQknHQ7+lsUagMGDLB0DPTvNisry/PtAxDbCBwDYNu6deuMlStXnnT65ZdfbN0AP/3000WuO5Dp4MGDQb1U0odpfbE3c+bMkJwZR44cMXr06GHrmFxyySW22mBn2wSO2dOvXz/Lx/7YsWNGOLj5BZCv6YorrjAfgJ2iD/pOvPAONpBt586d5sO41W0mJSUZa9asidlrdu3atS21S6/t2dnZAX0H8+bNc+y81GCOQGlHk9XvXH9bghHL5zf7HLogEu0ke/TRR/3+LekLirS0NNvbGzx4sBFLnA4cO/vss43MzEyfAU333Xefo9s8MVWrVs0MEiuKXhs0eM3uds4880zbx91L9/gEjv2bvrSxe+517tw56N9WL/7mRvM9ZaTp9+lksLWdKT4+3rzeaiCwvtgOp2gKHHMiILVly5aG12hAi69jogHvXuLmPqFIBY699957jlzLKleubHz++ecBbVMDeNq0aePIdu+5556g91mXcWLbOuDt9ddf93uPsGvXLqNnz56ObDMWA8e8eA4OGzbMkW2XKlXK7Pfydw5qcFuvXr1ccw56df91EIqV7VSqVMnYu3evpWPt65iMGzfufwIpwxE49uqrr1o+5nPmzPF8+wDENgLHAISU3sBGw0jhOnXqmKPid+zYEfJtaXBL8+bNLR+TYsWK2cqOYOf7IHDMHn0YsjqCLFyiLXBMR0rpiyUdIeiG7+rEdP/991vetgYClC9f3vK2b7311pi9Zvft2zfk2YteeOEFx87PG2+8MaBt2smmdvrppwd9HL14fntxn50MIilevLgxa9asgLetAQNFjSANdOrSpYsRS5wMHNNrYSC/e9qBff755zu2XZ0aNmwYcKdx//79bf/G68hkO7x0jx/KwLG6deuaI7O/++4784WDBpdocOKBAweM9evXG99++605elyDTzTgKFIZx5wIlrzgggsCDjYPhBd/f6LhntIN9O8pVH+zVicNstUBOaEKso3mwLE33njD9vEN53O9G2iwir9j4lRmx2jh5j6hSAWOnXLKKbb/tho3bhx09kTNNH755Zfb3rbevwUTrKz3GBpsYne7OvBM+xHCfR2LxcAxr52D+hxpdeDinyd9ztq6dWtQ+6yBQnFxcRE9B728/99//72l7QwaNMgI9f3C888/b/Y1hCNw7KuvvopYlvBYaB+A2EbgGICQipYOYx2RHU5aPsTOcfn9998tb9vOdgkcs6dRo0aWjru+hAyXaAkc09FI119/vbF69WrHj8Hy5cttPci3bdvWdslMLRtjdfvp6emWUtVHwzXbznEZOnRoQNvQjC9OvmgPhB43q9sItlPFi+e3F/fZySASfYlsJRuEZiezs91y5coZscSpwDEt6xBMMJUT2Y5OTFrOI5jfXe0Atpt9Tv9+7fDSPX4oAsf0hcinn34aVDs0CGDUqFFm2dJQtvfvNMDK7v5qSUm7wYp/5tXfn2i4p3QLO6XKQz1p5j3NxBtK0RQ4pqXhnTiuTg94cjMt0+XrWGhJXa9xc59QJALHdHCXE5lwfWXh9Rf0r/fWdtugAQ/h+F0+MZUtW9ZYtWpVRDMtxUrgmBfPQX22t7s9fVZfu3atpX3WEsWRPAe9vP9aStPKdjToNFyczmx2MnPnzrV8zJ999lnPtw9AbIsXAIBUrFgxrEfh7LPPtrXNhQsXOtoehMeWLVssLVe1alXH2xLt2rZtK1deeaXUqVPH8XW/99572utpefmXX35Z4uLibLWhZ8+e0qBBA0vLZmVlySeffCKxSK+dVo/tb7/95nce/d5///13ccr69etl27ZtfuebNm2arWMSDC+e317cZyc9+uijQZ9n6p577pHExETL2927d6/s27fP8vKxKCEhQUaPHi1JSUkBL9OpUycpWbKkI9t/+OGHgzqPK1SoIOeee66tba5atcrW8tzjW3f99dfLypUr5YorrghqudKlS8vdd98td9xxh4TLoEGDZPjw4bbWceONN8rHH38c1N+XP/z+wJ/XX39dTjnlFFceqKlTp5rPXP369ZNjx46J1zn1e6L3dV6xYMECn5+feuqp4jX0Cf3Vhx9+aPuYjhw50nKfWUpKiowZM0aSk5NttUHvHwL1+eefi13PPfecNGzY0PI9U8eOHW23IVZ48RycMGGC2KX33fXq1bO07H333Wc+o0aKl/f/+PHjlpbbtGmThEvZsmVDvg0771k2b94sXm8fgNhG4BgAROLiGx8vTZo0sbz8kiVLHG0PQm/37t2WO4kJHPtfs2bNkksuuUSqVasmr732mhQUFIhT7HTktWvXTtq3b+/INeKqq66yvPyXX34psUiDEJo1a2Zp2T/++EPy8/N9zrN8+fKAAlX0pXKgL48CCVizGjiWnp4uHTp0CGoZL57fXtxnp9SsWVPuv/9+S8uWKVPG9gvB7du321o+1txwww1Sv379oM89J17M6vX3zjvvDHo5u4FjgQTfukms3OP379/fDHqy+xIrHB566CHzBaodAwYMkLffftsMznQSvz/wp3jx4vLDDz9I06ZNXXmwNPD+jTfekNatW8u6devEy9LS0hxZj5cCx/wNePRa4Bh9Qn9VWFgo33zzja1jeuaZZwYd4P53Gvxh5R73z+bNmyeZmZl+59N+q8mTJ9valv7d9OnTx/LyOiDqpZdesj0wKhZ48RxUP/30k61tacC7Ppfa8cILL0ikeHn/U1NTLS2nz0mx1Dej/blWBzmGI4jO7e0DENsIHAOACKlUqZLlZRk9EH127Nhhedly5co52pZYsmvXLjOjhT64L1q0yPb6NLOJnZcivXr1Eqd07tzZVoaAWM0MYCXzkdLjMX/+fNtBXqpNmzYBt8NfUNjWrVtl48aNYsUZZ5wR1Et9L57fXtxnJ2nQmNXORdW8eXPb13j8l2Z9scJqRoI/u+6668xg1WA1btzYc+dAtN/jaxYKJzIthoNmwXvmmWdsryMUL1D5/UEw14zp06dL165dXXvQVq9eLaeddposW7ZMvEqzwjghNzdXvMJf4FirVq3ES+gT+t+MdBpMZzfQPZL32H/2448/BvQ3ceDAAVvb0QAjHahghwYD6zXd67x4Dm7YsMFy/9MJ2gdr9xx0aoBesLy+/1azee3Zs8cctKrZ2vwNyI0G+v3pQMdw/5bHSvsAxDYCxwAgQuyM4I+27Av4d9CKVVZe1HqNZoo6/fTT5auvvrK1npkzZ0YsMOTvrKY9V3l5eeaIw1h0zjnnWF7WX2BYoIFjOqpUJycCx+yUqQz2WHjx/PbiPjtFRzhqiU07atSoYWv5w4cPBzWyUgM/wjWFeyRnlSpVzKBVKzQ7p109evSwtJzdktLBnANuEc33+JpRZ+zYsbZfhoSrjO6wYcNsrUODzp566ikJBX5/EGyJV33h++yzzzqW2cppWkK6e/fuMZVxIhg5OTmOrMdOQH400d/v9evX+5zHaxnH6BP6q9mzZ9s6nhkZGZbvT0/2nGb3fAxkf/wFUwYSwHrZZZeJE6699loJJzc+q3nxHLTbp6DZeS+99FJxwpVXXinh5vX9r1WrluVlddCrZtHXbFhXX321WaL1559/Nv/WNHtftLF6vx2uAZ1ubx+A2OX+3kAAcImjR4+a5fHeeustefDBB82H7LPOOsvMpqEv5EqWLGkG+GgJs0AeYseNG2e5LTrSA9HFzo27W18euPEYX3755fL1119bXoedjqNixYrZKk/ldKY5u51gbqXXXaspu/0Fhmm2B6cDxzTjiK9RrIEGqzkROObF89uL++wUDZorX758RPfZqZe0seC8886znBHJ7veg97ea4dCKUqVKuf4c4B7/v3r37i0NGjSQaGAn4Ev/ll599VUZNGiQhAq/PwiWBmw+8MAD5oAYfSHnxgBODRrTbKxawtJrnCox6ZVBYZoN3Nd5opn27GTojEb0Cf3VnDlzbB3PLl26OPr3dOGFF4Z8fxYvXmxrG506dTL7np3gVMBTNPPiObhkyRJb29CsU05Vxbj44osl3Ly+/7Vr17b9fL5//3755JNP5N5775Vu3bqZ69S/A800rvt03333mWXOp0yZYg46cCu3B2a5vX0AYpe1t24A4AE6WuL333+Xb775xrzZ1Y4vt4ygyM7OjnQTECQ6CcND/0a1nJb+7bZs2TLo5VeuXGnrxbOOPnOLFStWSCwqUaKEmXXnjz/+CHpZPS/0HDnZi7i1a9cGlEFBlz3RYatBNYEE8mpw2BVXXOFoxjFNWx7sOe7F89uL++wULZ9gV/HixW0tr5nWYL/sp2aysUMDiawG7Np9mRKKc4B7/KLdeuutEuv0uv7OO+/IDTfcENLt8PsDq/QF3McffyyDBw+WUaNGyYcffuhY0JITfv31V7N94c5WE2lOlf7xSuCYv8xKXss2pugT+t/nbztOOeUUcVKLFi1Cvj9aJs8OK31cvjJD6zOC3dKZ0cyL56CWnnbLPmuWNf1NDOc9jtf3XwfP6GBcOwOuiyrDrYNmdSoqc7qWx9XBaFqi02rfgpcCs9zePgCxK/JXaABwGQ0CeO2118zMYm4tw0DgWPSx8yAYTRnH9IFw8uTJfufT0ccalHHo0CEzrfX8+fPlp59+st2RduIh6frrrzeDPYN9GN28ebPEiljal5Nl2rISOHbw4EFZtmzZSTvkAs38pR1FJ0b5aqfHF198YTlwbOfOnbJmzRqxOro12EwUsXROBLovXtxnpzjxYkLLd9jhxYwmRWnUqFHE7iPsbFtL6rjlHOAe339wYqtWrSSWaRlRDXhxqsyTL/z+wC7Neqp9EsOHD5fPP/9cxo8fbw44OH78eMQP7mOPPSbXXHON5UyY0UhLNNlVtmxZzxwzf4Fjsf574+U+oXD9TtoZVBGK9en3q9l1fGUjyszMjGhg0cnWZ3UgWyzw4jm4bds2W9to2rSpOEV/DzVLlfYHh4vX91/17NnT8cAxX/TdmiZl0Elpf+q5555rlr286KKLIlbC22ogf7gC/dzePgCxy315zwEgQrQUzpNPPmnWex8yZIhrg8ZUfn5+pJuAML74jKYX51qqVV8w+5v04bht27bStWtX6du3r7z++uuybt06+fHHHx0pDaclXnSdwWYgsduJEGsvN9wq2BKNgQSIBRo49ucSlYGWqyyqM9ZOJ+3ZZ58d1PxePL+9uM9O0uu0E78JcEadOnUsL2u3M9bOtt2Ae/zAaDbNWKYv3fWFRTiCxvj9gZP0BdtNN91kDrLRF8I6aGHAgAFm4E2kMqPqc9sPP/wgXqLPl3bVrFlTvGLBggU+P/dixjGv9AkFoqCgwBxEZTc7o5OcWJ+/wLBdu3bZWn/16tXFSdWqVROv8uo5aPddh2bJcpLT6/PH6/uvdFCrDvqOFB1A/tlnn8mVV15ptuPBBx+0fW0M5+9quKoRub19AGIXgWMA8J90zpoqV8tBEJmPULBTksIrGeZ0tFW3bt3MTmYdwW7X448/HtSIfM1Upp1HsUIfxmNVx44dLY+6djJwTFO8B2Lp0qUnLQFhJ3As2OA5L57fXtxnJ5UqVcqR7D5wrkyvVXYDC+yWHI0k7vEDpwH9sUzvC7t37x6WbfH7g1DR6/Gll14qL730kvnMpNl0tXTkU089JT169JAKFSqE7eB/+umn4iVz5861vQ4dpOgFWrLKX7leLwaO0Sf0199Juy+37dwbF/XcYvfZRbPq+2K3v9npe3Knj2E08eo5aLdPIdrPQa/vv9JzTO8b3UD7SZ999lkzgE4z7IYz6Mnquxa7WfVjpX0AYheBYwA8T8vZdejQQZYsWeL5Y4HQoZMwuLJW48aNM8sA2qEj8r///vuA54+1oNFY25+/nyNWM6NMnz79pKMytWRqIP58Xmpph0CCa3Sk2Mm2azVwrGrVqtKwYUNPnw+B7I8X99ltnZiRyoQSi+x0AAZb1vbvihUrJtGIe/zIlj9ym6FDh8rMmTPDsi1+fxAuen3W8uUPP/ywmVFPMzasX79ePvjgAzOrcygzWWimaK/Yv3+/39KLgahbt654gQ6a8ZUlv3Tp0p4Jovsz+oScHRwZioENdtfp7/ff7n47HWTi5cAxr56DmonZTfsc7udMr+//CX369AlLFuZgAh4feOABueCCC8ygTjc/r4UrMMvt7QMQuwgcA+BpWvZJ66prRyD8c2rkh90HtWhEJ2Hw5c1GjRplZiGz4/333w9qZHQsifVMdVbLVWo5gjVr1lgK4NLSfeXLl/9LMEagAWx/34YGNvobie/kvnvx/PbiPrutE9PuNRzu6AC0cw8TKdzjB69s2bISy/SFxPnnny/z5s0L+bb4/UEkaXnh6667TkaPHm1mXdywYYOMGDHC8ayCWu7JbsmnaPHdd9/5DIQKVLt27cQL/JWp1DKrXkSf0H8Fkxk+VKXYT8ZqVvNw/f7bHQzyd14e5OPVc9DuOer0c2G4n3G9vv9/9t5775mDD9xEByVcfPHFjtxzhap/LVx9I25vH4DYReAYAM/SDDBXX321+fIe4Q0ci+USeqF4GIy1rAWB0vIVp512mq11BFp+8EQWq1i7xsUyq4FjJzsvAg0c+3OZymDLVf59m/r/W/2OrOy7F89vL+6z215MePllhNtfFEXLtq3gHt+akiVLSqw7fPiwWa4y1Jmm+f2Bm9SuXVvuu+8+mTNnjpl1z8499N+tWLFCvGDMmDGOrEcz3XuBv+xsXg0co0/I2d/JUPST2c104y+QyG6gkb8yhMHyYt+s189BHaTrpsFs4R4c5/X9//tv0qRJk6Rfv37iJlqCXTNFe70UpNvbByB2RVcPMAA4SDMRhatcSaxwYkTWiZc2XlOpUiXLy3o5uNHui419+/bJxo0bA5qXUTnRpXXr1gGViTyZv5eNDDTA8GSBYyf7b0W9QPnztc9qmUp19tlnB72MF89vL+4zAO7xrfJKuSLNNN21a1fLWT8Dwe8P3EoH5fzyyy/y3HPPOZbdMdZplsKTlZwPVvXq1aVatWriBf4Cx3SAmBfRJ+Ts7+SRI0dsr8PpdfrbL7v77fQ+h+IYRguvnoN2M5o5HbwY7nPQ6/t/sgDK1157TaZOnSpt2rQRt9D71ED78q0oKCiwXH3Izm95rLQPQGwjcAyAZz399NOOrEc7//r37y/jx483O8h2795tjhDSbAe+pt69e0u0cSrtemZmpnhN5cqVJTk52dKy27ZtE6+qX7++7XUEmlVCR+WQHSd6aAaczp07W1r2z4Fies1evXp1QMudLEhMA9gCGdGlD/4zZsywHTjWsGFDSy+dvHh+e3GfAXCPb1ViYqJnTp89e/aYgxPWrVsXkvXz+wO3u//+++X222+3vZ4DBw5IrNNsbU645JJLxAv0mcff87dXA8foE/prcIvd+w6ns2Vpdhe75dH8ZW+tUKGCrfU7Pah0586d4lVePQeLFy/uqkAnpwOx/PH6/hdFKynMnTtXJk+eLD179gxJGdZgExeMHDkyZOvXa5/er1hRs2ZNCTW3tw9AbCNwDIAn/f777wEHChSlbNmy8vbbb8umTZvk1Vdflauuukpatmwp5cuXj9lR5nZTZisdMbFlyxbxmri4OKlRo4alZb0cOKZ/T3Zp1rFAA5GqVKlie3twf0Y6vW6fyJAQaLYxLfNzsoAt7Wzs2LFjQOs4sS19ybZ06VIJV7Yxr57fXtxnwOu4x/cOuy9fd+zYYd5HbN68WZzG7w+igZYBsluKOJIllsJB+3sCfVbw5/LLLxcvWLVqlc/zQgNrGzRoIF5En9B/6bWnatWqto7n2rVrbX8nTq9PMwv6Ynefly9fLk4KdeluN/PqOWg3G5HT983aNxdOXt//QPobP/nkE3OA7aeffio33XST1K1bNyJt+fjjjy0HT4XyPUutWrUk1NzePgCxjcAxAJ40ceJEW8vrw+WsWbPMG2ir2UycHpkUDk6MrFm0aJF4ldVRH14OHHPiIfHgwYNhecDS0i/+Mg2Ge4p1dkqZnngJZKdMZSCf/dmJLGNa7qawsFDCvc9ePL+9uM+Al3GP7x0//PCD36wK/uhgFn1BEop7bX5/EA3Bl5o51w67gWdupgEVAwYMcOxF9RlnnCFe4K9M5SmnnBLT540/9An9l9WBlSdYHYgVqvXpPYm/+xIdjOaWfdbsq17OOObVc9BusNyyZcvESU4HQ/rj9f0PJjPbFVdcYQbQa4ZmvVboc/awYcPkhhtuMAfPVqxYMaRt0AyL8+fPD8m67Tz7hSOjl9vbByC2efdJDYCn6Ut7O0aPHm27hJ4+pEeCnVTcTrT5m2++Ea+y2kmk2YmysrLEi5xIxR/MsWvUqJGtDgQCO8KrcePGljNKRSJwbN68eeb5aDVzgb5k6dKli1jlxfPbi/vsVRqkEc4gPkZyupOX7/G9plWrVvLtt99KWlqarfVs2LDBDMretWuXOInfH0QDuy+XYjXTumZ96d69u2MZ1e644w7PlE/3Fzim124vo0/or8/yoTzXwj3INZDf/RYtWtjaxowZMywPQPu7H3/8Ubz+rObFc9Duc46TgVNaBSDcg+q9vv9WaZDY+eefLw8++KCMGzfOvBZpMJmW2tSAx6+++kqGDx9uJlho3ry5YwHic+bMkVDIzMy0vGw4+oHc3j4AsY3AMQCepOnzrdK0+nqzbIc+xDqd0jpQKSkplpfdvn27rU4KzR41fvx48So7nUR2ztlotnLlStvrCOaFRvv27W1l5NORWAgvq6UbNbhAs9EFOqrTV3CYnjepqal+15GXl2dmqzyReSxYWg65TJkyYpUXz28v7jPgZV6+x/cizeCjZVTsDIxRq1evlq5duwZc3jwQ/P6gKBqM9NFHHzn28t+O/Px8W8uXKFFCYs3MmTPNa4tTmXg0uLVfv37iFf4CH0499VTxMvqEnPmdVDoYa//+/eIUu4NcA9kfu4GT2ierZdmdoL9DXufFc9Bu8KKefxos5IRJkyZJuHl9/52m5aebNWsml1xyifzzn/80M5Rpxla9h3r11VdtZ/UL1XO11T4DDYjTwLhQc3v7AMQ2AscAhJTdUZXHjx8Xp2m2FztZjJwoMbB48WKzXnyk0g1blZuba+sl+ieffOL4aP5o0qZNG9ekQI8WkydPtr2OYsWKBVWazg59eRnN3HjNDlXgmAYlfvHFFwG9tKtcubLUq1fPZ0Buu3btAtrud999Z3lkqp0ylV49v724z4BXef0e36suvPBCeffddyUuLs52BoFzzz03qBLnvnj99yca7ynDRZ+pr7vuOvNFmz4fRzKAbP369baWr169usQKDaLTEkya3dfJPotbb71VypYtK17hr9/C7kv7aEef0H916NDB1rHUQVn6PO8EfT5fs2ZNyPdHv/9g+qdO5r333hO7Nm7cKD///LPt9UQ7L56DdoN3c3Jy5PvvvxcnfPbZZxJuXt//cClfvrz079/fPK/tBDLZKdnoiwa3WdGwYUNb79VipX0AYhuBYwBcm93qRIk+p2kGETsqVKhguw0TJkyQSLFbg37KlCmWltMROQ888IB4mWYLspoRwcl02NFi9uzZZmm/cJZgadKkieXyEer999+P6tJ2brxmhzKY6plnnglovkBKUQZarlLLoGn2xUgEjnnx/PbiPgNe5fV7fC/TIJyXX37Z9nr05cZ5551n+1xSXv/9icZ7ynDTQQxXX321+ZLnlVdekWPHjoV1+ytWrLA9OMluqUs30L8zfXmrz+oPP/ywo0GL5cqVk8cee0y8QrM2+irXrAG+em30MvqEnPudVC+99JLlZ+s/e/HFF20tr/183bp18ztfUlKSdO7c2da2NFjebv/gvffeazvjZCzw4jmo+2z3vcCYMWPEicB1q+8X7PD6/oebVkwYMWKE5eWdyu72d1avoXaCv2OpfQBiG4FjAELK7kiqUATL2O0ItPsiQTvBNV1vpFSrVs3W8hr0YOUlxl133RWykSLRQstUWO0o9VrGMf07veeeexxZV/369YOa//LLL7eVTlo78iJFSyA+8sgjMXXN9kdTn/vKBuZE2vNAgsLOOuusgNZl9aVgcnKynH766WKXF89vL+4z4EVev8f3ujvuuEOGDh3qyMAFzWKmGezs8vLvTzTeU0aKZvQeMGCAmb1LX+aHY981y9ndd99tax36HdetW1eilWZ2efLJJ80yxVdeeaUsX77c8W089dRTUrp0afGKTZs2+fy8UqVKkp6eLl5Gn9BfXXrppbaOp/aTvfXWW7bWoYMV7Wbx0v6CQDML2rk3UBqkpJl8rN73aqbLr776ylYbYonXzkEN4NXy7Hb88ssv8sMPP9hax6BBgyISvOj1/Y+Ejh07Wl42FMdo69atljNMt23bVkLN7e0DEPsIHAMQUtopZKdjSNP/ZmdnO95RY7cEjR1a8/3w4cMSKTqi2Y758+cHPWpWM42NHTvW1nZjRfv27cOapjgaaervXr16yaxZsxxJjx3sCELdth16voe7JOvUqVPN8ko6enXGjBkxdc0ORyYuJwLHtDNERxCH8tqRkZFhez1ePL+9uM+AF3n9Hh8i//rXv2TgwIG2D8X06dPlkksuMUsK2uHl359ovaeMJA0+HTlypFnSR+/7NPuIvjwKxbNWnz59zBefdmiZ9vh493YrawkxDQjesWOHmU1Qy8U/99xzcv3110utWrXMfpHBgwebgXuhoJlfbrnlFvESfwMF7Q5ijBX0Cf3XDTfcYPt4aqZAq/1let3V66HdDJ96XQnUFVdcYfu5Xu9TNNtqsKWO9brvxDGPJV49B+3S4HOr2WE1cPHzzz+XSPH6/us9djgH9uv9mFVO9IE6+X5F731Dze3tAxD73PuEDyBm2Okc0pvw22+/3dFyATri087L/ZkzZ8qGDRssLfv222/LO++8I5Fkp7b8CToyd8iQIX7TcWdmZpoj9ocPH257m7FCX8RYoR3e/kbwRjvtKNFRW6eeeqpjpZ70pZeOKAtGixYtbI1A27t3r/k967+hpC8zP/roIzMVdZcuXWy//HHrNTvSgWM6arNp06Z+59OXo3ruun0fvXh+e3GfAS/y+j0+/u2FF15w5CWgXoM1K4idlx1e//2JxntKt5gzZ44ZBKmZdfUlkAZFakkjDfqySgMM9BlL71e1FKpddjN2OGHz5s3ms97JJs3WW6JECalSpYq5zz169DAzfHz44YfmcqGk2/zggw+Cfg6Ndv4yZHgp+5ov9An91ymnnGK7dKOed927dzczdQbj0KFDZn+l3WyDWur82muvDSpbowZ92aUldjXruZY99kfvZTQr6wUXXODZ39WiePEc1PNASwjazdqpv6vBBvnroIRg2hoKXt//jz/+WOrUqWMGLGqm5VCzMxBFB4M77ffff7e0nN7DhKMUpNvbByD2JUa6AQBin47k1BtqqzRds46m6tmzp9nhp52nOuLA34sh3e7JOuoSEhLMDERW26TBUv369TNHaCQmBn4Z1dI1Wq4x0pwodaYBPtrp8OWXX0rfvn3NTuMTLwY0wGnFihVmp/TXX3/tSJmXWOsk1HPQX9Ddyfz222/m6Gg30w6pQDtLjh49ambm2Lhxo5maXYPGnA6Ou/rqqy0t99BDD9l6aabp6jVLlV6/nH5w06x/ul59GbF//36J9Wt2IPQlpy5rd5RmUdfMQNulHbeh6nhxMjjOi+e3F/cZ8Bqv3+Pj3/Q3WwP59GWcPovYoeeC3ktqWadgzok/8/LvTzTeU7rR3LlzzemJJ56QlJQUadasmfmiWweE6TVPS1xqCUA9NjqQQfddS6Nrti19tlq9erX50m7ixImOZrDT8o74X/od6TUjFC873c5f34/+TiP2+4SCpQGdmu3Sjp07d5q/E1odQUv++vud0PsDLXHtRNYdDfLVv/tgM4rqvYqVc+DvAQb6e6CBMBrs3rp16///PdDrvQbJarbF8ePHy5YtW2xtK5Z57RzUwOqbb77Z9iBvvbfQc04Hz3To0MHnvHquP//88+bxsRME7wSv77/SANJx48aZk95P6qAbzcTm9O+L3o8+8sgjlpfXcuJO099Rq5lkw3Ef4/b2AfAAAwBCbPDgwfomP+xTdnZ2kW3q1auX7fVffPHFxt69e/3uf2ZmpnH99dc7vn921KxZMyLfiROTtj3aderUydK+33zzzSFvWzSfG3+fKlasaOTm5lo+FpdeeqntNiQkJBh33HGHsXLlSsvtOHTokPH9998bAwcODOj7Oeuss4xYu2YHomXLliFp1/PPPx9wG7777ruQtCEjI8M4fvy44SQvnt9e2+fHHnvM1r46YcqUKbbaMHbsWCNW9O7dO2LfR6S/Bzvb1uMWDC/f47vhb95N7dX7is6dOzvynVxzzTVGQUGB5X312u9PtN9ThtqBAwciclycnM444wxHjkUsPXvqlJiYaHz11VeGV7311ls+j0/79u0j3UTXcGOfUCTvI8477zzH/g5Lly5t3j++9957xi+//GIsXrzYmD59ujFhwgRj0KBBRp06dRzbll7DrP7m6HcZ6WuW3Wnjxo1GrPDaObh9+3YjJSXFkTbEx8cb5557rjFmzBhjyZIl5nNUTk6OsXnzZuP33383Hn74YUf32Ylz0Mv7f9111xW5vlNPPdV48MEHzfP26NGjhh3z5883WrVqZWv/pk6dajjp2LFjRlJSkqW2vPvuu462JRrbB8AbyDgGIOR0hLTbnHfeebbLM3zzzTdSr1496d27t5x//vlmKRJNdawZl3Sk0eLFi815NH2427Ju6SgSHemCyNDzxUqq5mnTpoWkPbHq0UcfNUeSWTVq1CgzQ4SO1rdKR5VpJhKdTjvtNDMFvmaLaNKkiZQqVUpKlixptlHTm+tILM3YpyVe161bJ0uWLDGvIzrZHYka7dfsQDNyLVq0KKLHQ7OTxcfHm6WAnG6DnfJrJ+PF89uL+wx4jdfv8fFfqamp5vekWUk1s5bdki66Ps0OYiWTlVd/f6L1nhKBZWfBX2mWh7Fjx8oll1zi2UNTvHhxn58vW7bMvEalpaWJ19En9L+/k61atQq67FtRpY5PZNIJtZEjR5r3B1YMGzZMvvjiC7O9iDyvnYOVK1c2My3rftul/V8///yzOUULr+9/URYsWGBOzzzzjHlf07hxYzOTnmb+ql+/vlltRkujli1b1jzvNNOdPlvoM/Hu3bvNiiJabl0ritgpUam03HjHjh3FSbNmzTKf6YOlz39ajjbU3N4+AB4R6cg1ALFPM/6UKlUqJCMrfE2+RtzoqInixYuHvU1OTnboCJhIt9/LGccWLVpkef+3bdsW0rbFyqjv5s2bO5Kh6dNPP434vgQ72c0O4cZrdiAmTpzoeJv0dyI/Pz+odtgdUXeyacSIEUYoePH89tI+uyH7UKQzXbkJGcfCk3HMy/f4bvibd2N79+zZYzRq1MiR76Zfv36W99dLvz/Rfk8ZatGecezMM8907FjEyrOn/u5oNj+v08wq/o7VgAEDIt1MV3Bjn1Ck7yP8Zaxz23TbbbfZ3mfNEBPp/bAzxVLGMS+egwcPHjQqVKjg2XPQq/vvK+OYmyY7z11OZ0Nu27at422JxvYB8Ib4SAeuAYh9OvK5Z8+e4iYZGRly++23R7QNkaw7rvXrzz333IhtX0eNeNkpp5wizZo1s7Tsd99953h7Yk16erqZGcKJDE2ane+BBx4QL3HjNTtSWbl0dFuw1+pQZNfQbGqh4MXz24v7DHiJ1+/x8b/KlStnZgCoUaOG7cPz+uuvy7333mtpWS/+/kTrPSWKppkl3nzzTQ7Rn1SvXl1+//13ueCCCzx/XLSPQ7Mv+/Lyyy9Lt27d5Mcff5SjR4969pjRJ/S/brnlFunTp49EA834qZme7NLstjfccINEQunSpeXaa6+NyLbdymvnoGar1Uy2XuX1/Xcz7du95557HF/vt99+a2m56667TsLB7e0D4A0EjgEIi/vuu891L1EefPBB80VCJLRr106uvPJKiaSnn37ab6deKPTt21cuvfRS8bpevXpZWu6rr75yvC2x9nCppaOaNm3q2DqfffZZM4W5l7jxmh1IsED79u0dXaeVIDCnA8c0Bby+WAgVL57fXtx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A+jKrqjw+fdnC3tNwk2w/3RwfeWpndGeSr2QHAAAAAAByT3EMBlhje2fvSWMHW7K7uuf1i6bHqxZMy/lcAACQjUsmjY73r67NKvurQ6fiC5v2WiwAAAAAAAwCimMwgJo7u+OGR7dGXVNrVvk/njsl3rJkZs7nAgCAc/HSmknx51n+csM3dxyMf6o/YsEAAAAAADDAFMdggLR1dcd7H98WW041Z5V/8awJcePKmkhlcQ0QAADk29uXzYprp43LKvuZtfXx9NHGnM8EAAAAAAA8O8UxGADt3em46fHtseZYU1b5q6eOjQ9ePDcKlMYAABiket6r3vacebFwTGVitjuTifc/sT32nMnu5F0AAAAAAKD/KY5BnnV0p3s/JHsqyxMWLp5YHZ987oIoKvCvKwAAg1t5UWF89oqFMbGsODF7prM7bnx0azS2d+ZlNgAAAAAA4L/SRIE86kqn4wNP7ojHDp/OKr907Ki48/JFUVroX1UAAIaGSeWl8dkrFkVZFu9h9ze3x/ue2N77yxUAAAAAAEB+aaNAnnSlM/Hhp3bFrw6dyipfW10e91y5KCqLC3M+GwAA9KdFY0fFxy6dH6kssmuPn4lPPrM7MpmMhwAAAAAAAHmkOAZ50J3JxMef3hU/P3Aiq/y0itK476olMbo0+YofAAAYjJ43bVxct3x2Vtkf7zseX9myL+czAQAAAAAA/5fiGORYOpOJTz2zu/fDsGxMLi+JB65ZEhPLSzwbAACGtFfPnxovq5mUVfYvtx2IHzYczflMAAAAAADAf1AcgxzquW7njrX18S97jmWVn1hW3Fsam1ZZ5rkAADDkpVKpuGnVnLh4YnVW+dvX1MWTR07nfC4AAAAAAEBxDHJaGrt7fUP8Y/2RrPLjSovj/quXxsxR5Z4KAADDRnFBQdx+2cKYNaosqyveb3liR+xqbM7LbAAAAAAAMJI5cQxyWBr77u7DWeXHlBT1njRWU600BgDA8FNdUhT3XLm4931vkuau7nj3o9viWGtHXmYDAAAAAICRSnEMclAa++y6+qxLY9XFhfH5q5dEbXWFZwEAwLA1Y1RZfPaKRVFakErMHm3tiBsf3RrNnd15mQ0AAAAAAEYixTHoR+lMJu5YWx//UJfd9ZSVRYVx39VLYsGYSs8BAIBhb/n4qrjt0vmRXB2L2NHYEh94ckd0pTN5mAwAAAAAAEYexTHox9LY7Wvq4gf12ZXGKooK4t6rFsfisaM8AwAARowXTB8f71w+O6vs40dO957m23OqLwAAAAAA0L8Ux6CfSmOfXlMX/9RwNKt8WWFB3H3l4t4TFwAAYKR51fyp8Ue1k7PK/mP9kfjmjoM5nwkAAAAAAEYaxTG4QN2ZTHzimd3xwyxLY6WFBXHXFYti1YRquwcAYERKpVLx7pVz4qopY7PK379pb/x03/GczwUAAAAAACOJ4hhcYGns40/vih/tOZZ1aezuKxbFJZNG2zsAACNaUUEqPvHc+bFoTGVW+Y89vSvWHW/K+VwAAAAAADBSpDKZTGagh4ChqCv9H6WxH2d58kHP9ZT3XLkoVk9UGgOAoSTTfjK6677bZ6aw9hWRKh2Xt5lgODne2hFveHBjHG7pSMxWlxTF169dFrOqyvMyGwAAAAAADGeKY3AeOtPp+MhTu+LnB05klS/vKY1dtdj1lAAA8BvUNbXEmx7cFGc7uxP3M6OyNL72/OUxtrTYLgEAAAAA4AK4qhLOUVtXd9z02PasS2MVRQVxr9IYAAA8q9rqivjMZQujMJVK3NL+5vZ4z2Pbet+XAwAAAAAA509xDM7B2c6uuOHRrfH4kdNZ5SuKCuPeq5bEygnV9gwAAH24ZNLo+MDFtVntaPPJs/GBJ3f2Xh8PAAAAAACcH8UxyFJje2dc9/CWWHv8TFb5yqLCuO+qxbFifJUdAwBAFl4ye1K8afGMrHb1yOFTccfaushklMcAAAAAAOB8KI5BFo63dsRbf7U5tp5qzmpfo4oL4/NXL47lSmMAAHBO3rB4Rrxk9sSssv/UcDS+vnW/DQMAAAAAwHlQHIMEh5rb4y0PbYq6ptasdlVVXBj3X70klo5z0hgAAJyrVCoVt6yujUsmZnfd+1e37o9/qj9i0QAAAAAAcI4Ux6APe860xpsf2hT7m9uz2tPY0qL4wjVLY/HYUfYKAADnqbigIG6/bGHUVpdnlf/M2rp45NAp+wYAAAAAgHOgOAbPYsfp5t6Txo62dmS1o0nlJfGla5bFgjGVdgoAABeoqqQoPnfl4phYXpKY7c5E3Prkjth08oy9AwAAAABAlhTH4Dd4+mhjvPWhzXGqvSur/cyoLI0vP29p1GR5IgIAAJBsckVp3Hvl4hhVXJiYbe9Ox42Pbou9Z7K7Yh4AAAAAAEY6xTH4b36y73i865Gt0dzVndVueq7P+fLzlsW0yjK7BACAfjZ3dEXcefnCKC5IJWYbO7ri+ke2xom27E4NBgAAAACAkUxxDP5TJpOJb+04GB96amd0ZTJZ7WXx2Mr40jVLY0IW1+cAAADnZ/XE0fHR58yP5OpYxKGW9nj3o9uiuTO7XwQBAAAAAICRSnEMIiKdycQ9Gxrivo17st7HqglVcf/VS2J0abEdAgBAjv3WjPHx7pU1WWW3n26O9z+xPTrTac8FAAAAAACeheIYI157dzo++OTO+Ptdh7PexeWTx8Tnrlwco4qLRvz+AAAgX/5k3tT48wXTsso+dbQxPvHM7t6ThQEAAAAAgP9J64URramjK25+fFusPX4m69e8YPq4+Nil86O4QO8SAEaCTPOB6Fp7W5+ZolW3Rapyet5mgpHs7ctmxbHWjvjxvuOJ2R/vPR6TykriHctn52U2AAAAAAAYSjRfGLGOtLTHmx/cdE6lsT+cMzk+fukCpTEAABggBalUfPCSuXHppNFZ5f92x8H47q5DOZ8LAAAAAACGGsUxRqRtp87GG365MerPtGb9mrctnRk3r5oTRQWpnM4GAAD0ref039svWxgLx1Rmtaq71zfEz/Ynn1AGAAAAAAAjieIYI87P95+INz+0OY61dWaVL0yl4sOXzI3XLZoRqZTSGAAADAaVxYVxz5WLYmpFaWI2ExEfeWpXPHXkdF5mAwAAAACAoUBxjBEjk8nE17fuj1uf3BHt3emsXlNRVBB3X7koXjJ7Us7nAwAAzs34spK496rFMbqkKDHblcnEzY9vjy0nz1ozAAAAAAAojjFStHV3x4d/vTO+smVf1q8ZV1ocX7xmaVw2eUxOZwMAAM7f7KryuOuKRVFamPx7Ua3d6bjh0a3R0JT9lfUAAAAAADBcOXGMYe9gc1u86Zeb4if7TmT9mlmjyuLrz18Wi8aOyulsAADAhVs+vio+een8rH7Abezoiusf2RJHWtqtHgAAAACAEU1xjGHticOn47U/3xA7Gluyfs3ycaPiq9cui2mVZTmdDQAA6D9XTxsX71tdm1X2SGtHXP/I1mhs7/QIAAAAAAAYsRTHGJYymUz89bb9vdfQNHV2Z/26500bG/dfvSTGlBbndD4AAKD//cGcyfGWJTOzyjacaY0bH9sWrV3Z/7wAAAAAAADDieIYw87p9s54z2Pb4oub90XmHF732oXT4/bLFkZZUWEOpwMAAHLp9YumxyvmTskqu+nk2Xj/E9ujM532UAAAAAAAGHEUxxhW1h5rij/7+YZ49PDprF9TXJCKj1wyL96+bFYUpFI5nQ8AAMitVCoV715ZE78zc0JW+SeONMbHnt4V6cy5/NoJAAAAAAAMfUUDPQD0h+7eqykPxNe27ItzOStgbGlx3Hn5wlg+vsqDAACAYaLnF0I+dMncaOroisePJP9SyU/2nYgxJcVx48qa3uIZAAAAAACMBE4cY8jbd7Y13vrQ5vjKOZbGFo2pjL9+wXKlMQAAGIaKCwri05ctiGXjRmWV/+7uw/FX2w7kfC4AAAAAABgsFMcYsjKZTHx/9+H4s59tiA0nzpzTa//X7InxlWuXxZSK0pzNBwAADKzyosK4+8pFMaeqPKv8l7fsix/UHc75XAAAAAAAMBgojjEkHW5pj+sf2Rp3rKuPtu7szxkrSqXifavmxAcvnhulhf7xBwCA4W50SXHce9XimFJRklX+jrX18fP9J3I+FwAAAAAADDTNGYaUrnQ6vrnjYPzJT9bFU0cbz+m1E8tL4kvPWxp/WDslUqlUzmYEAAAGl8kVpXHfVUtiTElRYjYTER/59c749Tn+vAEAAAAAAEON4hhDxvrjTfGan2+Iz2/cc06njPW4asrY+NZvrYjl46tyNh8AADB4za4qj3uuXBzlWZw83JnOxE2PbYtNJ8/kZTYAAAAAABgIimMMiWspP/rrXfHmhzbH7qbWc3ptz9WUN6yoic9esTBGlxbnbEYAAGDwWzJuVNxx+cLenxOStHan492PbI3djS15mQ0AAAAAAPJNcYxBq7GjM+7b0BB//O9r41/3Hjvn18+oLI2vPX9Z/On8qa6mBAAAel06eUx87NL5kc3l9U2d3fHOR7bE/rNttgcAAAAAwLBTNNADwH/X1NEV3687HN/acTDOdHaf14JeXjs5rls+OyqKCi0YAAD4L35rxvg43T4n7lhXn7iZE22dcd3DW+Ir1y6NSeWlNgkAAAAAwLChOMagcaSlPf5u16H43/VHoqUrfV5/xqTykvjAxXPjsslj+n0+AABg+Hj53ClxqqMzvrplf2L2UEt7vPPhrfHl5y2NMaXFeZkPAAAAAAByTXGMAdWdycSvjzbGvzQcjV8cONn7f5+v35s1MW5cWRNVJf6xBgAAkr1h0YxobO+K7+4+nJhtONMa73pkazxwzZIYVexnDgAAAAAAhj7/tZu8y2QyUdfUGj/dfzx+tOdYHG3tuKA/b9aosrh5VW08Z9LofpsRAAAY/lKpVLx7ZU2c6eyKf9t7PDG/7XRzvPexbfG5qxZHWWFhXmYEAAAAAIBcURwjLxo7OmP98TPx2OHT8djhU3HkAstiPUoKUvG6RTPizxdMi5LCgn6ZEwAAGFkKUqn44MXzoqWrOx46eCoxv/b4mbj1iR1xx+ULo6jAzyEAAAAAAAxdimP0m7OdXXGirTOOtXbEibaOONjSHttONcf2081xqKW9Xzd9zdSxcf2K2TFzVHm//rkAAMDIU1SQio9fuiDe8+i2+PWxxsT8o4dPx22/3hUfvXR+FKZSeZkRAAAAAAD6m+IYF3zt5PfrjsQPG472FsRybcX4qrhu2axYOaE6538vAABg5CgtLIg7rlgY1z28JTafPJuY/+n+EzGquCjet2pO75WXAAAAAAAw1CiOcUHu27gnvr3zUM63WFNVHm9fOiuumTbWhzIAAEBOVBQVxj1XLoq3P7QldjW1JOb/sf5IVBUXxjuWz/ZEAAAAAAAYchTHOG/1TS05L40tHTcqXrNgWlw9bZwrYAAAgJwbXVIc9129ON784KbY39yemP/bHQdjVElRvHbhdE8HAAAAAIAhRXGM8/aLAydztr0rpoyJ1yyYHhdNqHLCGAAAkFfjy0ri81cviTc/tDmOtXYk5r+waW+MKiqMl8+dkpf5AAAAAACgPyiOcd4KU6l+3d6UipJ4yexJ8ZJZE2P6qLJ+/bMBAADOxbTKsvj8VYvjrQ9tjtMdXYn5O9fVR0VxYbx41kSLBgAAAABgSFAc47zNG11xwdsbU1IUV0wZG783e2JcPLE6Cvq5jAYAcMEKiiMqpiZngGFnTnVF3HvV4nj7r7ZEc1d3n9lMRHz86V1RVlgQz58+Pm8zAgAAAADA+UplMpme/74N56znH53rHt4STx9ryv4fuIhYNLaytyzWcx3l4rGj+v3kMgAAgP609nhTvOvhLdGeTv7xuSiVijsuXxhXTh3rIQAAAAAAMKgpjnFBGjs6494Ne+JHe479j/9fdUlRTC4viQVjKmPhmMpYNKYy5o+pjIqiQlsHAACGlMcOn4r3PrY9urP43avSglTcfeXiuGTS6LzMBgAAAAAA50NxjH5xqr0zDjS3Rc9nKOPLimN8WUmUFhbYLgAAMGz8bP/x+OCTO3uvpUxSXlgQ9129JFaMr8rDZAAAAAAAcO4UxwAAACBL/1R/JD61pi6rbGVRYTxwzZJYPHaU/QIAAAAAMOg4EgoAAACy9LI5k+Ndy2dnlW3u6o7rH9kauxtb7BcAAAAAgEFHcQwAAADOwasWTIs3L5mZVbapoyuue3hL7D3TascAAAAAAAwqimMAAABwjv5i0fR4zYJpWWVPtnfGOx7eEgeb2+wZAAAAAIBBQ3EMAAAAzlEqlYq3L5sVr5g7Jav80daO3pPHjra22zUAAAAAAIOC4hgAAACcZ3ns3Str4vdrJmaVP9DcHu98eGucbOu0bwAAAAAABpziGAAAAJzvD9WpVNyyem68aOb4rPINZ1rj+ke2RGOH8hgAAAAAAANLcQwAAAAuQGEqFR+5ZF5cM3VsVvmdjS1xwyNb42xnl70DAAAAADBgFMcAAADgAhUVFMQnn7sgLps8Oqv8llPN8Z7HtkVrV7fdAwAAAAAwIBTHAAAAoB+UFBbEZy5bGKsmVGWVX3f8TLz3sW3RpjwGAAAAAMAASGUymcxA/I0BAGAoyLQeja6t9/eZKVp8XaTKJ+VtJmBwa+7sjnc+siU2nzybVf7SSaPjs1csitJCv9sFAAAAAED++K/SAADQl3RnRMuhvv/qyQD8p8riwvjclYtjweiKrHby1NHGeN/j26OjO22HAAAAAADkjeIYAAAA9LPqkqK47+olUVNVnlX+8SOn49Ynd0RnWnkMAAAAAID8UBwDAACAHBhbWhz3X70kZlSWZpV/+NCp+OCTO6NLeQwAAAAAgDxQHAMAAIAcmVheEvdfvTSmVJRklX/w4Mn4yK93RVc645kAAAAAAJBTimMAAACQQ1MrS+MLVy+NSeXZlcd+tv9EfOzpXdGdUR4DAAAAACB3FMcAAAAgx6aPKosHrl4SE8qKs8r/+77j8clndkdaeQwAAAAAgBxRHAMAAIA8mFVVHl+4ZmmMK82uPPajPcfi02vqlMcAAAAAAMgJxTEAAADIk9lV5fHANUtibGlRVvkfNhyNO9fWR8bJYwAAAAAA9DPFMQAAAMij2uqKuP/qJTG6JLvy2A/qj8Rd6xuUxwAAAAAA6FeKYwAAAJBn80ZX9pbHqosLs8p/b/fhuHfDHuUxAAAAAAD6jeIYAAAADIAFYyrjvquXxKgsy2Pf2XUo7t+0V3kMAAAAAIB+oTgGAAAAA2Tx2FFx71WLo6Iou/LYN3ccjPs2OnkMAAAAAIALpzgGAAAAA2jZuKr43JWLorwwux/Rv73zkGsrAQAAAAC4YIpjAAAAMMBWTqiOe65cHGVZlsd6rq28Z0ODaysBAAAAADhvimMAAAAwCKyaWB13XbEoSgtSWeX/ftfhuGu98hgAAAAAAOdHcQwAAAAGiUsmjY47r1gUJVmWx763+3Dcua4+0plMzmcDAAAAAGB4URwDAACAQeS5k8fEHZcvzLo89v26I3HHWuUxAAAAAADOjeIYAAAADDKXTxkbd16e/bWV/1h/JG5fU+fkMQAAAAAAsqY4BgAAAIPQZVPGxGevyL489k8NR+NTa3YrjwEAAAAAkBXFMQAAABikLp08Ju6+cnGUFmb34/s/NxyLTzyzO7ozmZzPBgAAAADA0KY4BgAAAIPYJZNGxz1XLoqyLMtjP9pzLD7+9C7lMQAAAAAA+qQ4BgAAAIPcxRP/ozxWnmV57N/2Ho+P/Vp5DAAAAACAZ6c4BgAAAEPA6p7y2FWLo6Ioux/lf7zveNz2653RlXZtJQAAAAAA/5PiGAAAAAwRqyZUx+euzL489pN9J+KDT+2IznQ657MBAAAAADC0KI4BAADAELJyQnXce9WSqCgqzCr/ywMn4+bHt0dbd3fOZwMAAAAAYOhQHAMAAIAhZsX4qrjvqsVRmWV57LHDp+PGR7dFS5fyGAAAAAAA/0FxDAAAAIag5eOr4vNXL45RxdmVx5451hTXP7wlznR05Xw2AAAAAAAGP8UxAAAAGKKWjquK+69eElVZlsc2njwb73h4S5xu78z5bAAAAAAADG6KYwAAADCELR47qrc8Vp1leWz76eZ42682x/HWjpzPBgAAAADA4KU4BgAAAEPcorGj4gvPWxpjS4uzytc1tcZbHtoch1vacz4bAAAAAACDUyqTyWQGeggAAADgwjU0tcZ1j2yJY1meJjaloqT3tLKZo8qtHwAAAABghFEcAwAAgGHkYHNbvONXW+JglqeJjSstjnuvWhwLxlTmfDYAAAAAAAYPxTEAAAAYZo60tMd1D2+JvWfbssqPKi6Mu65YFBdNqM75bAAAAAAADA6KYwAAADAMnWjriOsf3hq7mlqyypcWFsSnnrsgrpo6NuezAQAAAAAw8BTHAAAAYJhq7OiMGx7ZGltONWeVL0xFfPiSefG7sybmfDYAAAAAAAaW4hgAAAAMY2c7u+LGR7fF+hNnsn7Ne1bWxCvmTc3pXAAAAAAADCzFMQAAABjmWru64+bHt8dTRxuzfs0bF8/o/SuVSuV0NgAAAAAABobiGAAAAIwAHd3p+NBTO+PBgyezfs0fz50SN66siQLlMQAAAACAYUdxDAAAAEaI7kwmbl9TFz9sOJr1a140c3x8+JJ5UVxQkNPZAAAAAADIL8UxAAAAGEEymUw8sGlvfGPHwaxf85yJo+P2yxfEqOKinM4GAAAAAED+KI4BAADACPSN7Qfi/k17s87PG10Rn7tycUwsL8npXAAAAAAA5IfiGAAAAIxQP6w/Ep9eUxfpLPNTKkrinisXR211RY4nAwAAAAAg1xTHAAAAYAT75YET8aGndkZnOpNVvqq4MO68YlGsmlCd89kAAAAAAMgdxTEAAOhDpv1kdNd9t88dFda+IlKl4+wRGLJ+fbQxbn58W7R0ZXf2WElBKm57zvz4rRnjcz4bAAAAAAC5oTgGAAB9yDQfiK61t/W5o6JVt0Wqcro9AkPalpNn44ZHt0ZjR1dW+VRE3LCiJl45f2rOZwMAAAAAoP8V5ODPBAAAAIaYJeNGxdeuXRbTKkqzyvdcbHnPhoa4b0NDpDPZXXMJAAAAAMDgoTgGAAAA9JpVVR5fe/6yWDSmMuuNfGvnofjAkzuiravbFgEAAAAAhhDFMQAAAOD/GF9WEl983tK4fPKYrLfyiwMn422/2hwn2jpsEgAAAABgiFAcAwAAAP6LiqLC+OwVC+P3ayZmvZktp5rjL365MXY2NtsmAAAAAMAQoDgGAAAA/A9FBQXxgdVz442LZ2S9ncMtHfHmBzfFo4dO2SgAAAAAwCCnOAYAAAD8RqlUKt60ZGbcuro2ClPZLamlKx3vfWxbfHfXIVsFAAAAABjEFMcAAACAPr1szuS48/JFUVaY3X9GSEfEXesb4s61ddGVztguAAAAAMAgpDgGAAAAJLpy6tj40vOWxviy4qy39Q91R3pPHzvb2WXDAAAAAACDjOIYAAAAkJXFY0fFXz5/ecwbXZH1xh4/cjre+MtNse9sqy0DAAAAAAwiimMAAABA1qZUlMZXnrcsrpwyJuvX1J9pjdf/YmM8ceS0TQMAAAAADBKKYwAAAMA5qSwujDuvWBR/Mm9K1q8509kd735ka3xrx8HIZDI2DgAAAAAwwBTHAAAAgHNWmErFjSvnxE0XzYnCVHavSUfEfRv3xG1P74q27m5bBwAAAAAYQIpjAAAAwHn7o7lT4u4rFkdlUWHWr/nx3uPxlgc3x5GWdpsHAAAAABggimMAAADABblsypj42vOXxdSK0qxfs+10c7z2Fxtj3fEm2wcAAAAAGACKYwAAAMAFq62uiK8/f1msGF+V9WtOtXfGO361JX5Qd8QTAAAAAADIM8UxAAAAoF+MLyuJB65eEi+rmZT1a7oymfjM2rr4xDO7oq2725MAAAAAAMgTxTEAAACg35QUFsQtq2vjpovmRGEqlfXr/rnhWLzpl5viwNk2TwMAAAAAIA8UxwAAAIB+lUql4o/mTonPX704xpQUZf26HY0t8dpfbIiHD570RAAAAAAAckxxDAAAAMiJiyeOjr9+wYpYMLoi69ec6eyO9z6+Pb6waW90pTOeDAAAAABAjiiOAQAAADkztbI0vnrtsnjhjPHn9Lq/2X4g3vXIljjZ1pmz2QAAAAAARjLFMQAAACCnyooK4xOXzo+3L5sVqXN43dPHmuI1v9gQG06cyeF0AAAAAAAjk+IYAAAAkHOpVCpeu3B63HXFoqguLsz6dcdaO+KtD22O7+w8GJmMqysBAAAAAPqL4hgAAACQN1dOHRt/81srYuGYyqxf053JxOc27In3PrY9GttdXQkAAAAA0B8UxwAAAIC8mlZZFl+9dlm8rGbSOb3ukcOn4s9+viHWHm/K2WwAAAAAACOF4hgAAACQd6WFBXHrxXPjQxfPjdKCVNavO9raEW9/aHP85db9vSeRAQAAAABwfhTHAAAAgAHzv2omxdeevzxmVJZm/Zp0RHx5y75418Nb40RbR07nAwAAAAAYrhTHAAAAgAG1YExl/PULVsTVU8ee0+t+fawxXv2zDfHkkdM5mw0AAAAAYLhSHAMAAAAGXFVJUdxx+cJ4x7JZ5/QfK061d8a7HtkaD2zaE13pnrPIAAAAAADIhuIYAAAAMCgUpFLxmoXT4wvXLI2JZcVZvy4TEX+7/WC88cFNsfdMa05nBAAAAAAYLlKZTKbnv68CAAC/QSbdGdF6tO/dlE+KVEH2BQcAkp1u74yPPb0rHj18btdQlhUWxI0ra+KlNZMilUpZNQAAAADAs1AcAwAAAAaldCYTf7fzUDywaW90nePvvV07bVzcuro2Rpcq9gIAAAAA/CaKYwAAAMCgtvnkmfjgkzvjYEv7Ob2u57rLD18yLy6dPCZnswEAAAAADFWKYwAAAMCgd7azKz71TF38/MCJc37tq+ZPjbctnRUlhQU5mQ0AAAAAYChSHAMAAACGhEwmE/9YfzTuWV8fHelzu7py/uiK+Ohz5sfc0RU5mw8AAAAAYChRHAMAAACGlF2NzfGhp3ZGXVPrOb2uuCAVb1kyM161YFoUplI5mw8AAAAAYChQHAMAAACGnLbu7nhg49747u7D5/zaFeOr4sOXzI2Zo8pzMhsAAAAAwFCgOAYAAAAMWY8dPhUff3p3nGzvPKfXlRUWxPXLZ8cf1k6OlNPHAAAAAIARSHEMAAAAGNJOtnXGJ5/ZHY8cPnXOr33upNHxgYvnxuSK0pzMBgAAAAAwWCmOAQAAAENeJpOJH9QdiXs3NER7OnNOr60qLoz3XDQnfnfmBKePAQAAAAAjhuIYAAAAMGzUNbXEh5/aGTsbW875tddOGxfvX10bY0uLczIbAAAAAMBgojgGAAAADCsd3en48pZ98a0dB+Pczh6L3tLYLatr43nTxuVoOgAAAACAwUFxDAAAABiW1h1vio89vSsONLef82tfMnti3LiyJkYVF+VkNgAAAACAgaY4BgAAfch0NEX60IN97qhg6rWRKqm2R4BBqKWrO+7fuCe+X3fknF87qbwkbl1dG5dPGZuT2QAAAAAABpLiGAAA9CHTfCC61t7W546KVt0Wqcrp9ggwiD1x+HR8Ys3uONbacV6nj92woiaqS5w+BgAAAAAMHwUDPQAAAABArl02ZUx8+4Ur43dnTTjn1/5oz7H405+ui4cPnszJbAAAAAAAA0FxDAAAABgRek4M++hz5sftly2IMed4etjxts547+Pb4yNP7YzG9s6czQgAAAAAkC+KYwAAAMCI8vzp4+Pbv70yrpk69pxf++N9x+OVP10fvzxwIiezAfD/b+8+4OQqy74B39uym94TUgkJvXdpgqJBioBgRV8BURELqIgNEFEU/awoiu1FxQ6+oEhVlKLSeydAQnrvfZMt3+85qYSd2Taz9bp+Hmd2zsw5z56Z8OzM/M99AwAAAG1FcAwAAADodgZX9YhvHbpLXHLghOhdXtasxy6uXh9feODFuOjBF2OJ6mMAAAAAQCclOAYAAAB0SyUlJXHC9sOy6mMHDe3f7Mf/c+aieM8/nog7ZiyM+vr6oowRAAAAAKBYBMcAAACAbm27XpXxw9fvFp/fb4foVd68j0qWrquJix96KatAtmjtuqKNEQAAAACg0ATHAAAAgG6vtKQkTh2/XfzhzfvGwcOaX33s7tmL4z13PBm3Tlug+hgAAAAA0CkIjgEAAABsNKJ3ZfzwiN3iov3HR+/ysmYdl+XrauIrj7wcn7r3+Zi9aq1jCgAAAAB0aIJjAAAAAFspKSmJk3YYHn+cuE8ctt2AZh+bB+Yti/fe8WT86aU5UVtf79gCAAAAAB2S4BgAAABAA4b3qozvHbZrfPnAHaNvRfOqj62prYvvPzU1Pnz3MzFl+WrHFwAAAADocATHAAAAAPJUHzt++6Hxp4n7xpEjBjb7OD27eGW8/59Pxc+fmxHrauscZwAAAACgwxAcAwAAAGjEkJ494luH7hJfPXin6N+jvFnHq6a+Pq5+fma8/19PxVOLVjjWAAAAAECHIDgGAAAA0MTqY28ZMyT+OHGfeLpuNswAAH6cSURBVOOoQc0+ZlNXrImz734mvvPEK7Fqfa1jDgAAAAC0K8ExAAAAgGYYXNUjvnnILnH563aOQZUVzTp29RHx58lz473/fCLum7vEcQcAAAAA2o3gGAAAAEALvGn04PjTMfvEW7cf2uzHzl29Lj597wvx5YdeiiXV6x1/AAAAAKDNCY4BAAAAtFD/HhXxpQN3jCuP2C1G9qps9uNvn7Ew3vOPJ+L26Quivj7VIwMAAAAAaBuCYwAAAACtdPDwAfGHifvEe3ca0ewPW5auq4kvP/xyVoFs7upqzwUAAAAA0CYExwAAAAAKoGd5WXxy73Fx9Rv3ih3792r24++ftzROu+OJ+ONLc6JW9TEAAAAAoMgExwAAAAAKaPdBfeKao/eKc/YYExWlJc167Oqaurjiqalx1p1Px/NLVnpeAAAAAICiERwDAAAAKLDy0tL4wK6j43dv2if2Gdy32Y9/YemqLDz2/SenxuqaWs8PAAAAAFBwgmMAAAAARTKuX8/46VF7xOf23SF6lZc167F1EfGnl+fEe/7xRPx79mLPEQAAAABQUIJjAAAAAEVUWlISb5+wXfxp4j5xxHYDm/34eWvWxWfvnxSfv39SzF9TXZQxAgAAAADdj+AYAAAAQBsY3qsyvnPYLvG1g3eKgZXlzX783bMXx7v/8WRc9/KcqK2vL8oYAQAAAIDuQ3AMAAAAoI2UlJTExDFD4tqJ+8bxY4c2+/Gra2rju09OjQ/d9XS8uHRVUcYIAAAAAHQPgmMAAAAAbax/ZUV8+aAd4wdH7Bajelc2+/HPLVkVZ975VPzgqalZmAwAAAAAoLkExwAAAADaySHDB8QfJu4TZ+4yKspKSpr12Nr6iD+8NCfe848n4q5Zi6Je+0oAAAAAoBkExwAAAADaUVVZWXx0z7HxuzfvHXsP7tvsx89bsy6+8MCL8al7n4/pK9YUZYwAAAAAQNcjOAYAAADQAYzv1yt+dtQe8YX9xkffirJmP/6Becvivf98Mn767PRYq30lAAAAANAIwTEAAACADqK0pCROGT88rj1m3zhmzOBmP359XX386oVZ8Z47nox/z16sfSUAAAAAkFNJfX19fe7VAADQvdXXrI76pc/lvU/JgN2jpLxXm40JgO7jgblL4/89PiVmr65u0eMP325AfGafHWJUn6qCjw0AAAAA6NwExwAAAAA6sNR28uoXZsbvX5wTtS04/69HaUmcscuo+J9dRkZVWfNbYAIAAAAAXZPgGAAAAEAn8PKyVfHNx6bE04tXtujxo3pXZtXHDh8xsOBjAwAAAAA6H8ExAAAAgE6irr4+/jZ1fvz4memxfF1Ni7Zx5IiB8am9x2lfCQAAAADdnOAYAAAAQCezrHp9Fh5LIbLmN6/c0L7ytJ1GZi0se1doXwkAAAAA3ZHgGAAAAEAn9cziFfGtx1+JSUtXtejxQ6oq4mN7jo3jxg6N0pKSgo8PAAAAAOi4BMcAAAAAOrHa+vr465R58ZNnp8eK9bUt2sbuA3vH+fvsEHsN7lvw8QEAAAAAHZPgGAAAAEAXsKR6ffzo6Wlx87QFLd7GW8YMiY/vOTaG96os6NgAAAAAgI5HcAwAAACgC3lqUWpfOSVeWra6RY+vLCuN9+88Mt6388joVV5W8PEBAAAAAB2D4BgAAABAF1NTVx83TJkbP312RqyqaVn7ykGVFfHh3cfESeOGRXlpScHHCAAAAAC0L8ExAAAAgC5q0dp1ceXT0+K26QtbvI1xfXvGx/YcG0eOGBglJQJkAAAAANBVCI4BAAAAdHFPL1oR339yajy7ZGWLt7HvkL5x7l7bx56D+hZ0bAAAAABA+xAcAwAAAOgG6urr4/bpC+PHz0yLhWvXt3g7bxo1OD6655gY06dnQccHAAAAALQtwTEAAMijvmZ11C99Lv8f1QN2j5LyXo4jAJ3C6prauOaFWfGHl2bHurr6Fm2jrKQkThw3NM7adXQM71VZ8DECAAAAAMUnOAYAAHnUr5oVNY9fmvcYle93aZT0HuU4AtCpzF61Nq58elrcOWtxi7dRUVoSp+wwPM7cdVQMrupR0PEBAAAAAMVVWuTtAwAAANABjexdFd84ZJf4yZG7x879W1Y5c31dfVw3eW6ccvvjWQhtaXXLW2ACAAAAAG1LcAwAAACgG9t/aP+45k17x6UH7Rjb9WpZ1bDq2rr43Yuz45TbH4ufPTs9VqyrKfg4AQAAAIDCEhwDAAAA6OZKS0riuLFD47pj9otP7Dk2+lSUtWg7q2vq4pcvzMoCZL94bkYsW6cCGQAAAAB0VCX19fX17T0IAADoqOpXzYqaxy/Ne5/y/S6Nkt6j2mxMAFBsy6rXx68nzYo/T56btaNsqV7lpXHq+O3ivTuNiMFVLatmBgAAAAAUh+AYAADkITgGQHc2e9Xa+OmzM+LvMxa2ajuVpSVx4rhh8T87j4oRvSsLNj4AAAAAoOUExwAAIA/BMQCIeH7JyvjZszPi/nlLW3U4ykpK4tixQ+LMXUbF2L49HVoAAAAAaEeCYwAAkIfgGABs8cTC5VmA7LGFy1v3gVREvHHUoHjvTiNjr8F9HWIAAAAAaAeCYwAAkIfgGABsMzfW18cjC1KAbHo8vXhlqw/PnoP6ZAGyo0YOivLSFCkDAAAAANqC4BgAAOQhOAYAOebI+vq4b+7S+NlzM2LS0lWtPkwjelXGuyZsFyftMCz6VJQ77AAAAABQZIJjAACQh+AYADQeILtn9uL4xXMz4+Xlq1t9uHqVl8VJ44bFu3fcLkb2rnL4AQAAAKBIBMcAACAPwTEAaJq6+vr475wl8esXZsWzS1rfwjI1rTx8u4Fx6vjhcch2A6KsRBtLAAAAACgkdf8BAAAAaLXSkpI4cuSgeP2IgfHw/GXxq0mz4rEFy1u8vfqI+O/cJdmS2lieMn54nLj9sBhUVeHZAgAAAIACUHEMAADyUHEMAFruqUUr4lcvzIz75i4tyGEsLymJo0cPilPHbxf7Du4bJaqQAQAAAECLCY4BAEAegmMA0HqTlq6KX78wM+6atTirJFYIE/r1jJPGDY9jxw6JAZWqkAEAAABAcwmOAQBAHoJjAFA4M1eujWtfnhM3T5sfq2vqClaF7PUjB2ZtLF83fECUl5YUZLsAAAAA0NUJjgEAQB6CYwBQeCvW1cSNU+fHdS/PiXlr1hVsu0OqKuL47YdmIbKxfXsWbLsAAAAA0BUJjgEAQB6CYwBQPDV1dVn7yj+8NDueW7KqoNvee3DfeOv2Q+PoUYOjb4/ygm4bAAAAALoCwTEAAMhDcAwAiq++vj6eWrQi/vTynLhn9pKora8v2LYrSkvi8O0GxlvGDskuK8tKC7ZtAAAAAOjMnG4JAAAAQLsqKSmJfYb0y5YFa9bFjVPnxV9fmZ9db631dfVx9+zF2dKnoiyrQPaWMUNi/6H9orSkpCDjBwAAAIDOSMUxAOhAVq5cGU8++WQ8++yzMXPmzJg/f36sXbs2amtro6qqKvr37x+jRo2KHXfcMfbbb78YPXp0dGbLly+Pl156KWbNmpX9vrNnz44VK1bEqlWrorq6OiorK6N3797ZMmTIkOz33mmnnWLChAnRo0ePNhtnTU1NTJkyJaZPn56NMy1LlizJxrlmzZrsi85N4+zXr1/ssMMOm8c6aNCgNhsnxaHiGAC0j5q6+rh3zpK4fsrceHD+soJvf1jPHnHMmCHx5tGDY9cBvbO/6QAAAACgOxEcA4AOYN68efHXv/417rvvvli/fn2TH5fCSSeeeGIcdNBB0RmkANYzzzwTTz/9dDz33HNZECu1JWqunj17xhFHHBHHHHNMFqQrhhQOe/zxx7MQ36RJk7IgW0vsscce2TgPOOCAKC3VFqkzEhwDgPY3Y+Wa+MuUeXHTtAWxfF1Nwbc/qndlvGn04Jg4ekjs1L+XEBkAAAAA3YLgGAC0oxSauvHGG+Mvf/lLswJj29prr73inHPOiYEDB0ZHU1dXF0899VQ88MAD8cgjj8Tq1asLuv1DDz00PvCBD0SfPn1ava1U8SyNMy0pOFZIw4cPj7PPPjt22223gm6X4hMcA4COo7q2Lu6ZvThumjo/Hp6/LJp/CkLjxvSpyqqQpSDZjv2EyAAAAADougTHAKCdpApWP/zhD7OqVoUwYMCAuOCCC2L8+PHRkcyYMSM+//nPF3Uf6Xf/8Ic/nLXvbI2LLrooXnnllSiW1P7o2GOPjdNOOy3Ky8uLth8KS3AMADqmuaur45ZpC+KWafNj1qqWVYdtzPZ9qrIA2ZtHD4kJ/XsVZR8AAAAA0F70SwKAdrBu3br4zne+U7DQWLJ06dK4/PLLY+rUqdHdpN89Hc8777wzOnqFudtuuy2+/e1vZ68BAABabrtelfHB3UbH/71lv7jqyN3j+LFDo7KssB91TVu5Nn75wqx47z+fjPf844n43+dmxJTlha2gCwAAAADtRakLAGgHv/71r+PZZ5/NuX7EiBHxxje+MXbfffcYOnRolJWVxYoVK2Ly5Mlx3333ZYGzFELaVmoDmQJUKUDWr1+/6AzS77bzzjvHLrvsEjvssEMMGzYsqyBWWVkZa9euzX7vVAXsueeey1pI5gpcpeNx9dVXR9++feOggw4qylhTu8k99tgjJkyYECNHjowhQ4ZEz549s32ncc6fPz8b54MPPhjz5s3LuZ2nn346rrrqqvjkJz+ZVSEDAKDlSktK4oCh/bPlM/uOiztnLorbZiyMxxcsL2gry1dWrIlfPD8zW8b17RlHjxoUR2tnCQAAAEAnplUlALSxFPz60Y9+lDNE9c53vjNOOOGE7HouL730UraNBQsWNLg+tWz87Gc/Gx21VWUKS+29995x2GGHxYEHHpiFr5pi2bJlccMNN8Qdd9yR8z69evWKb33rWzFo0KCCtKpMYbHXv/71ceihh2aBvqaoq6uL+++/P6655ppYuXJlzvudeeaZccwxxzR7nLQtrSoBoHOat7o6/jFjYdw+Y2G8vKx4VcLG9KmKo0cNzoJkuwzo7cQAAAAAADoNwTEAaEOpItgFF1yQtVbcVmlpaZx77rnxute9rknbStu47LLLYs6cOQ2u//SnP120ylstDY5VVVXF0UcfnYWlUmWxlnr44YfjyiuvjJqamgbXH3HEEfGxj32sVcGxvfbaK44//vgs4NbSqmCLFy/O2lJOmzYtZ8jtiiuuiD59+rRo+7QNwTEA6PwmL1sdt89YEH+fvjDmrSley/CRvSqzKmQpRLb7wD5CZAAAAAB0aKXtPQAA6E5uvfXWBkNjydvf/vYmh8aS1M7x/PPPz1o6NuSPf/xjVvmqI0hjPOmkk+IHP/hB/M///E+rQmNJCsSdc845Odffe++9sXDhwmZvNwXEUmAsBfK++MUvxj777NOqL/tS1bMUmkvtRnMFCfNVTwMAoDAm9O8VH99z+/jrcfvHT4/cI94+fngMrKwo+OGdvbo6fvfi7Djrrmfibbc/Flc8OTWeWrQi6hpoMw8AAAAA7U3FMQBoI2vXro3zzjuvwdaFo0ePjm984xt521PmcuONN8a1117b4Lq0v0MOOSTa06pVq2LdunUxcODAgm/7hz/8YTzwwAMNrnv3u98dJ598crO2N3PmzOy5KLQnnngia5/ZkNT+8rvf/W7B90nhqDgGAF1TTV19PLFwefxz5qK4a9aiWLqu4Wq2hTC0qiLemLWzHBx7D+kbZa04OQEAAAAACqW8YFsCAPK6//77GwyNJe94xztaFBpLjjvuuKyS2YoVK16z7p///Ge7B8d69+6dLcXwzne+M2dw7Omnn252cKwYobFk3333jZ122ileeuml16xLrUZTdbQhQ4YUZd8UQEXfKB1zYqP3AQA6l/LSkjhwWP9suWDfHeKxBcs2hMhmL47lBQ6RLVi7Pq6bPDdbBlWmENmgLES275B+2TgAAAAAoD0IjgFAG0ntE3O1MzzwwANbvN0ePXrEG9/4xvjb3/72mnXPP/98lw4lpWpdo0aNilmzZr1m3bRp06IjSc9xQ8GxTWPtqs9RV1DSo1+UbX9Sew8DACiiFN46ePiAbPncfjvEI/OXxz9nLYx7Zi2O5etrC7qvxdXr4/op87JlQI/yOGrkoDh69OA4cGgKkZUWdF8AAAAAkI/gGAC0gVQNLIW4GnLooYdGaSu/IDr88MMbDI7V19fHI488Escee2x0VePHj28wOJZaZK5ZsyZ69uwZHWWcuaRwX2dUV1eXva5TK85XXnkl5s6dmx33mpqa7LinUGT6vffbb7/Yf//9m11VL7V3feyxx+KZZ57JwnWLFi3KntO0nf79+2fb32OPPbJQ3tixY6OtVFdXZ2N68cUXY+rUqbFgwYJYvnx5dntJSUlUVVVlrVlTsDFVmksV51LAsdjmzZuXjSn9e0hL+jk9H+k4prGVl5dvHtvw4cNj3Lhx2fGbMGFCq/8b1FqrV6/OXkdPPfVUTJ8+Pfs3kZ7rioqK6Nu3b/Z8p9fSPvvsE7vvvntUVla263gB6NpSeOuQ7QZky+f3q4uH52+oRPbv2YtjRYFDZKk95o1T52dLv4qyODKFyEYNjoOH948KITIAAAAAikxwDADawLPPPpuFuBqSAjWtNWbMmKxiVUMBpNSysSsHx1KgJJcUmOkowbF840wBmY7gnnvuiZ/97Gevuf3II4+Mc845Z/PP6bV89913Z2HFFE5qSGrLmpYUAkr3TWGl0047LY444ohGx5FCWDfddFPWajUFnra1fv367LlN+07Btf/7v/+LvfbaK84888wsrFUs6Xe55ZZb4qGHHmpwXNv+7jNmzMju+/vf/z4LPZ100klx0EEHZeGyQli3bl08+eSTWTj0ueeey4J1jd0/Len4piBeGluSAnipamH670Sh2sqed955Df736Ac/+EEMHTp088/pOP31r3+NO++8M3tOt1VbW5vdnsJ5L7/8cvzjH/+IPn36xCmnnBITJ07MwnAAUEwpvHXYdgOzZX1dXTw6f3ncOWtR3D17cSwrcDvLVNns5mkLsqVPRVm8fsTALET2uuEDorJMJTIAAAAACs83LQDQBlKooyGpmk6qSFQIqQrPv//979fcnoI1qTJUe1cUag+FCugUW2d6bpYsWRI//OEPY9KkSc1+3FVXXZVVEEshtNRitSGPP/54Fl5L4abmSAHJL3zhC3H22WdnFfgKKY3lD3/4Q4P/vppqypQpccUVV2T/Tj/84Q9nFb9a4+c//3k8+OCDBQkdLl68OK6//vr4+9//HqeffnqTwn2FkF4L6fdo7nOdwma//e1vs7BZes4HDx5ctDECwLYhsk2VyD633/h4fOHyuHPmorhr9uJYUr2+oAdr5frauG36wmzpVV4aR2wMkR06fEBUlTeviisAAAAA5NJ5vqUEgE4shUYaktrrFapiTmo315BUrWfOnDnRVeWqspRCY7169YqOIl81qEJVeSq21P7wS1/6UrNDY1t74IEH4nvf+14WZtzW7bffHt/5zneaHSTauhLZT37yk7jvvvuiUFLwMoWTWhMa2zZEevHFF2dVCFvj/vvvL3iluhTISuG+X/3qVw0+P4V02223xXe/+90WP9ebXo9f+cpXcla9A4BiKi8tiYOG9Y/P7z8+bjnhgPjJkbvHOydsF0OqKgq+r9U1dfGPGYviCw+8GG+5+ZG48IEX458zF8bqmsK2zQQAAACg+xEcA4AiSwGM1LIuV3CsUPJtK7Wl66pS+7qGpPZ7uapadaRxJtttt110dKkq1Te/+c3ssrWeeuqp+NOf/vSq2+644474zW9+k7Ola3P+vaWKZYUIS6aKXpdffnksXbo0CmnVqlXxrW99K6uS1hGl5yJV9Cr29lv7XCepHWZqf5laWgJAeykrKYn9h/aPC/bdIW46/oD4+VF7xHt2HBHDehb+b9G1tXXxr1mL4qIHX4pjb3o4Pn//pPj79AWxcn1h22YCAAAA0D1oVQkAbVBpKlVCasiIESMKtp984aO5c+dGVzR16tRYsGBBsyqwtZeHH344Z5vKHXbYITqyFMb60Y9+9JqqaaNGjYqDDjoo9tprryyo17dv36zCXQrzpHDY3XffnTNoduutt2YtEVPgMVX1SqGxbSvG7bvvvtmy4447Rv/+/aOqqipWrFiRBTHT8bz33nsbrIyV/r2lqlkXXnhhi3/n1DLzyiuvzFt5a/z48bHPPvvEbrvtlrVL7NOnTzbuZcuWxezZs7NtPPTQQ7F69eoGx5haV1522WUxcuTIKIT035PU+jYd07QMGDAgevbsmVXeq6mpycaRnsNUAfGZZ57Jgmu5wlupbWU67oVu+5me62uuueZVt6Vjtscee2THcpdddsme63QsN403vZZSxbf0usr134Gbb745Tj755IKOFQBaorSkJPYZ0i9bPrn39vHckpVZO8s7Zy2OOaurC3pQq+vq4+7Zi7OlorQkDhk+IGtnmdpa9uvhIz8AAAAAGudTJAAosvnz5+dcN3To0ILtJ4UtKisro7q6ullj6Mz+8Y9/5FyXAkcdxQsvvBDTp09vcN3OO+/coVpqNiSFtLZ+XfXr1y/e8573xJFHHpkF37aWfpcUIku/11vf+tb49a9/3WCbxxTIuv766+OjH/1o1h5x64pRu+++e5x++ukNVtFL2x8+fHgceOCBcdxxx2VtLxsKFKVgVFr23HPPZv++KfSVgnK5QmMpnPXud787G2dDUuhpU6guHac///nP8a9//es190utJlM47Wtf+1qUlZVFS6RjlMJd6Xg0FkRNwb507NK403OTQpep8ltqe9mQFObbb7/9Cvr6TK+HrY/rrrvuGv/zP/+ThfC2lUJvKZCXXksnnXRSdhxvueWWBrd74403xlve8pYsXAgAHSlEtuegvtly7l7bxwtLV8WdsxZlQbKZqwobIltfVx//mbMkW8pLNrTRPHr04DhqxMDoX1n49pkAAAAAdA2CYwBQZNtWadpaqghUSCk81lBILN8YOqtZs2bFf/7znwbXpQDdwQcfHB3Ftddem3NdCl91dFuHxlLY8Ytf/GKT2mumEM/ZZ5+dBaQaqrj26KOPZm0lt359vuENb4gPfehDrwmkNWTcuHFZVbGLL764wapeKbDW3OBYCjX99Kc/zcbckBNOOCELgzU16JVCdh/84AezsaYqaNuG0VIb2dtvvz3bbnOkKm9vetObsipdLZWey3PPPTcLh6XfeduxpepuKZz5tre9LQolVaTb5Oijj46zzjqrSc91ajv7vve9L8rLy7OQWEPbfeCBB7LXDwB0RKnC5m4D+2TLx/YYGy8tW705RDZt5Zb5sRBq6uvj/nlLs+WbJREHDO2fVSI7auSgGFQlRAYAAADAFo1/SwMAtEoKX+QLlRRSru2tXLkyupLUXi+FcLauUrW1N7/5zR2mitc999wTkyZNanBdqsyV2jV2FumYppBWU0Jjm6RQ0JlnnpmF+baVgkoPPvjg5p9Tha4UNGtKkGiTNJZTTjmlwXUprLZ1UKmpz9fLL7/c4LpU9SqFl1pSHSyFvFKVsobcdNNNzR7n+eef36rQ2NbSa/CMM85ocN2dd96Zs51la/fZ1IDg1t7xjnfEmDFjGlzXUGU7AOioIbKdB/SOc/YYG9ces2/8ceI+8eHdRseEfj0Lvq/a+oiH5i+Lbz4+Jd566yNx3n+ei1umzY+V62sKvi8AAAAAOh/BMQAosnyhrdSKrZBybS9feK0zShWannvuuZxtAlPApyNIrQB/+9vf5lz/zne+M6ug1FmkcFFL2qsOHDgwDjnkkLz3SdX3UpCoJVIoK1WkaqhS2iuvvNLk7dTU1MQNN9yQs/VpruBXU6X2kA21t1y+fHncd9990Z5S2DK14NxWagP60ksvFXRfqV1mqjTWEim0l6sC2uTJk7PnEAA6W4hsfL9e8aHdx8QfJu4b107cN87ZY0zs3L9XUUJkD85fFl99ZHIcf/Mj8cUHJsXdsxZFdW3D7bkBAAAA6PoExwCgyPJVEkqt/Aop1/aaW82oI0vVoP74xz/mXH/aaadF3759o72lAMsPfvCDBlsoJrvsskunaFO5yciRI1tVHa2x1qHHHXdci5+39LrPVX1r6tSpTd5Oap3ZUFvXFFZ6//vfn32x2xrp8aeeemqHrJaVxpbCYw155plnCrqvFPxqzX/7DjjggAYfv379+pg5c2YrRwcA7Wtcv57xgV1Hx2/fvE/831v2jY/vOTZ2G9i74PuprquPO2ctjs8/8GIcf8sj8bVHX46H5y+L2iJUGgUAAACg4+o8JS4AoJPKVwGn0NWmcm2vq1ThWbJkSVxxxRU5f59UFeqNb3xjdASpleaUKVMaXJdCL+ecc06rg0ht6ZhjjmnVeMePH59zXUVFRauftwkTJmStKbc1bdq0Jm8jV3jrsEMPie361UX9qlm5H9xzWJSUVjS6j1RxLLVanDFjxmsCkak6YaqY115yhe+aU7WtKe10Dz/88FZtI1WXGzduXLzwwgsNPt9pHQB0BWP69IzTdxmVLbNXrY27Zi2OO2ctimcWF7YN/cr1tXHT1AXZMriqIiaOHhJvGTMkC6x1pr9XAQAAAGg+wTEAKLLa2tqc60pLC1v8M1VG6qrBsXXr1sV3v/vdWLx4cc52iB/5yEeiI7j55pvjrrvuyrk+telL7fo6kxTKa43+/ftnoaiGWrfuuOOOrQ5MjRo1qsHbly5d2uTXV67KWofsv0vUPH5p3seX73dpRO+Gx7CtPfbY4zXBsbq6upg0aVJWTau9pFBXZWVl1uJza4Ws4rXnnnsWJDA7duzYBoNjy5Yta/W2AaAjGtm7Kt6388hsmbe6enOI7KlFK6KQNcIWrV0ff3p5TraM7l0Vbxk7JI4ZPSSrhAYAAABA16NVJQC0I2fwN00K1Vx55ZU5K3ilwNx5552XhZPa2wMPPJC3lebEiRNb1fKxPQwYMCCGDRvW6u3ken522mmnom17zZo1TXr8Sy+9lLU63FYKUu25W+vHt7Wdd965wdubUx2tWBoK8OUKa7bErrvuWpDtpKBoQ3K1hgWArmR4r8p4z04j4udv2DNuOv6AuGDfHWL/of0K/iHfzFVr4+rnZ8a773giTv/XU/G7F2dnoTUAAAAAug4VxwCgyHJVAdtUjayQ7SpzVTcrdEvMtlRfXx+/+MUv4tFHH80ZvkuVxnbZZZdob0899VRcddVV2ZhzVe06/fTTo7PZbrvtCrKdFMIq1vZT+8/WBIlyhRJHjhyZ/fupKXAQryGzZ89u9bZTdbDJkydnFc3SkkJfa9euzQJ06TKFMJsrBerScezVq1erxzdixIgohJ49e7YqKAgAXcXQnj3inRO2y5ZFa9fFPbOXxF2zFsWjC5ZFbQFLkU1auipbfvT0tDhoWP84buzQeOOoQdGzPPd7HQAAAAA6vs77LTIAdBL5QluphWQhQ125WlJ25uDYb37zm7jnnntyrj/zzDM7RAWv1Dbv+9//fs7nYLfddotPfepTeYOEHVXv3r2LGhwrxPZzbTu1oGyKXKGtFBwrtL59+zZ4+5IlS1q0vRQOS/9G7rvvvpg1a1YUQzqOhQiOFfu1tG2bTQDoTgZX9YhTxw/PlqXV6+PfsxfHv2YtiofnFy5Eljbz0Pxl2fKtx0vj6NGD4/ixQzdUPCspKcxOAAAAAGgznfdbZADoJHJVQtoUcsi3vrlSRaHmjqEju/baa+Pvf/97zvWnnXZa1vqxvaVqVd/+9rdzhlZ23HHHuOCCC6JHjx7RGRUiMNRe289V/W1bixYtavD2e++9N1sa99lorVWrVjW7Etgtt9wSN954Y9EDUw218eyIryUAYIMBlRVx0g7Ds2VJ9fq4c+ai+PuMhfHkohUFO0RrauvilmkLsmV4zx5ZFbK0jOvXcGVQAAAAADoewTEAKLI+ffrkXJfav/Xv379g+8rVpi1XhaOO7K9//WsWiMnl1FNPjRNPPDHa2/Tp0+Ob3/xmzmO//fbbx+c+97mcrfU6g9QOtDNvvylWrCjcl6gt1dTqaMnChQuzsGJqR9mZdITnGgC6m4GVFfH2Cdtly5xV1XHHzIXxjxkL46VlTWvp3RTz1qyLX0+alS17DOwTx20/NI4ZPTj6V1YUbB8AAAAAFJ7gGAAUWb7Q1vLly2PEiBEF21faXnPDax1RqqJ03XXX5VyfAmPveMc7or2ltoCXX355rFy5ssH1o0ePji9+8Yud7vh3R80JbRVLbW1tk+6XWlpedtllsWDBgqKPCQDoWkb0rozTdxmVLVOWr84CZH+fvjBmry5c9dJnl6zMliuenBpHjBiYtbI8bMSAqCgtLdg+AAAAACgMwTEAKLLBgwfnXLds2bKC7ivX9vKNoaNJrSl///vf51x/7LHHZi0q29ucOXPi61//es6wXgoEXnjhhdGvX782HxvFC20VU1Paaqb7XHXVVXlDY2VlZTFhwoTYaaedYtSoUTF06NCssmFqE5na1paWlmZLQ1JL1VTNDADo+sb36xXn7DE2PrL7mHhm8cosRHbHzEVZa8tCqKmvj7tnL86W/j3K45gxQ7IQ2W4De6tCCgAAANBBCI4BQJGl0EYu8+fPL2horLq6utlj6Ej+9a9/xW9+85uc69/0pjfF6aefHu1t3rx5WWhs6dKlDa4fNmxYXHTRRTFgwIA2HxstU1HROdooPfjgg/Hss8/m/B1OPvnkePOb39ziwGJdXV0rRwgAdDaplfReg/tmyyf3HhePLFiWhcjumrU4VtcUJly/bF1N/Hny3GwZ17dnnDhuWBw3dkgMrupRkO0DAAAA0DKCYwBQZEOGDMkCHevXr2+walUhw0y5bLfddtHR3X333fHLX/4yZ9WlI488Ms4666xob6nSUwqNLV68OOfznUJjgwYNavOx0XI9e/Zs8PZU3e6Y1+8VNU98Le/jy/e9OEp6jWz1l7aNufXWW3O2xP385z8f48ePb9UYVq1a1arHAwCdW3lpSRwyfEC2fG6/2rhv7tKsleV/5yzJKogVwtQVa+LKp6fFVc9MjyNGDIgTtx8Wh243MNs3AAAAAG1LcAwAiiy1hBszZkxMmTLlNeumT59esP1MmzYt57px48ZFR/bf//43fvGLX+QMjR122GFx9tlnt3tLmxQWS6GxXK38Bg4cmIXGOkuFN7bIFfRbtGhR9KioiNLy/K+98oqKKOlR3IoZ6XX38ssvN7juQx/6UKtDYzU1NTmrFgIA3U9VWVkcPWpwtiyrXp+1sbx1+oJ4dvHKgmy/tr4+7pm9JFsGV1VkbSzfuv2wGNev4UA/AAAAAIUnOAYAbWCHHXbIGRxLYY3y8tZPyZMnT27w9qqqqhgxYkR0VA888ED89Kc/zRkaO/jgg+NjH/tYFsBrT6ktZQqN5Wov2r9//yw0Nnz48DYfG62X63mbO3duhzm8kyZNavD29O/7oIMOavX2O9LvCgB0LP0rK+IdE7bLlmkr1sSt0xbEbdMXxLw16wqy/UVr18dvX5ydLXsP7pu1snzTqMHRu6KsINsHAAAAoGHt+w0sAHQTu+++e4O3p/aVL730UkH28dxzzzV4+6677truoatcHn744fjxj38cdXV1Da4/4IAD4hOf+ES7j3/58uVZaCxXa9HUJjCFxkaObF2rQtpPrmpdL774YqxfXxMdQa7X3/7771+Q7affFQCgMdv37Rkf3XNs/PW4/ePHr989Tth+aPQsK9zf608tWhFff3RynHDLI3HZIy/HEwuX5zzJBAAAAIDWUXEMANrAHnvskbVZbOgLj8cffzx22223Vm1/xowZOdsn7rXXXtERpd/7yiuvjNra2gbX77PPPvHJT36yINXYWmPlypVx+eWXx6xZsxpc36dPn7jwwgtj9OjRbT42CmeXXXZp8N/o2rVr49kXXoo9O8DBTgHG5rTZbK5nn322INsBALqH0pKSOHBY/2z57L47xN2zF2eVyB6evywKEfNaU1sXN09bkC1j+lRlVchOGDs0hvQsbntwAAAAgO6kY5YfAYAupl+/flkwpSH3339/zopbTXXvvfc2eHsKwhx44IHR0Tz99NNxxRVXZG06G7LnnnvGpz/96XYPja1evTq+8Y1vZC1FG9KrV6/4whe+ENtvv32bj43CGjBgQOy4444NrrvrPw91iMOdK2TZo0frvzxdtmxZVgEQAKAlepaXxXFjh8aVr989bjxu//j4nmNjXN+eBTuYM1aujauemR4n3fZofObeF+LuWYtifSvfQwEAAAAgOAYAbeb1r399g7cvWrQoHnnkkRZvd926dXHXXXflbFM5dOjQ6Eief/75+N73vpe16WxIqr52wQUXFCQM0xpr1qyJb37zm/HKK680uL5nz55ZaCxXi0M6nyOPPLLB2x95/Jl4eW7Doa221Lt37wZvX7JkSau3/fe//z1nkBMAoDmG96qM03cZFX+auE/8+ui94l0Ttov+PQpzQkhtfcR/5y6Jzz/wYpx466Pxg6emxpTlqz1BAAAAAC2k4hgAtJFDDz00Z/Dj//7v/1pcdey2226LFStWNLjuzW9+c3QkL730Unz729+O6urqBtenqmyf/exn2z00lsaXxvnyyy83uL6ysjIbZ64KVXRORxxxRNZ6tCHX3LMu1q4vRNOlluvbt2/OMGZrTJs2LW6++eZWbQMAoKHqx7sN7BOf2XeHuOWEA+Ibh+wch203oGAfRi6prok/vDQnTrvjyTjrzqfjL1Pmxcr1gvAAAAAAzdG+/Z8AoBupqqqKiRMnxl//+tfXrJs5c2bceOONccoppzRrm7Nnz25we8nw4cPjda97XYvGmoJsN9xwQ4PrPvKRj8RRRx3V7G2myl3/7//9v1i7dm2D61MI63Of+1x2nNpTqoSWKqK98MILOUNjaZypmhtdS3pu3/72t8c111zzmnXTF9XFVX+vjk8eXxllpSVFqXCXqtjlM27cuAZvT6/VqVOn5lyfz8qVK+NHP/qRamMAQFFVlJbG0aMGZ8v8NdVx67SFcdPU+TFzVcPvDZrr2SUrs+X7T02No0cNihPHDYv9hvSL0pLC/90GAAAA0JWoOAYAbeitb31r9O/fv8F1119/fTz00ENN3tayZcviu9/9bs7qXaeddlqUlnaMqT4F477xjW/E6tUNt5FJ7R5T28fGgjPFllr1/eAHP4inn366wfUVFRXxmc98JmunSdeUqvTlaj/65PTa+OaNa2PRipZVB2zo9XbvvffGxRdfHLfffnuj909hxRRu21Z9fX389Kc/zfnvK5fU4vKrX/1qzJo1q1mPAwBojWE9K+PMXUfF/71l3/jpUXvECdsPjaqywrxvqa6ti9umL4yP/fu5eMffH49fPj8z5q1u+P0SAAAAAIJjANCmevXqFe973/saXJdaVV555ZVx0003Ndq2MrV8vOSSS2LOnDkNrt9nn33i4IMPjo4gjfHyyy/PKhs1ZPTo0VkYq7y8PNatW1fQpTntP9N9r7rqqnjssccaXF9WVhaf+MQnYueddy74OFOAiI5h0/Oc/q025MU5dfGl69bEjY+sixVrmt+6Mj3XKZj4q1/9Ks4777z48Y9/HFOmTGnSY1NwMVcVwenTp8dll12WhTSb8lq/884744tf/OKr7p+2394V/wCA7tXKMlUFu+TAHbNWlhfuPz72GtRw2/CWmLWqOn723Iw4+bbH4pP/fS7+OXNhrKstzAkAAAAAAF2FVpUA0MaOOOKIeOaZZ+Lf//73a9bV1tbGH//4x7j77rvj6KOPjt133z2GDh2ahVmWL1+eBUzuu+++LNyUqgw1ZODAgXHOOedER5EqKi1dujTn+hRc+fjHP16UfTenreaiRYvigQceyLk+PTff//73oxhSBbMvfelLRdk2zbfddttlYcZvfvObWevSba2qjrjhofVx06PrY88xZbHTiNLYudfkGLBdSfTu3TurCpZasqYKYGmZO3duTJs2LQt3TZ48udmVwbZ26qmnZv+m0utxW2kfqXLfAQccEAcddFDssMMOWYXD9KVs+u/HwoUL46mnnopHHnkk5s2b95rHv/vd784qn+VqJwsAUCx9Ksrj5B2GZ8sry1fHzdMWxC3TFsSS6tf+LdZc6V3TA/OWZUu/HuVx7JghWSvLnQf0LsjYAQAAADozwTEAaAdnnXVWFuJ47rnnclbp+v3vf9/s7aYqSSnwkqsdJtD0MF8KYaV2sLmCXutrIx6fWpstcf9P2+TQDhs2LN7xjnfEtddem7Oa2MMPP5wtzXHYYYfFcccd16SWmQAAxbRDv15x7l7bx0f3GBP3zl0aN02dH/fNXRK1zS/2+hrL19XEdZPnZssuA3pnAbJjxgyO/j0qCjF0AAAAgE6ntL0HAADdUY8ePeKCCy7IWkoWSgqLpaDL+PHjC7ZN6O7hsa9+9asxbuyo6EhOPvnkOPLIIwu2vVSdLFUpTJXJAAA6ivLS0jhq5KD4zmG7xk3HHxCf2HNsbN+ncG21Jy1dFd954pV46y2PxsUPvhgPzlsadTmqOgMAAAB0VYJjANBOqqqq4rOf/WxWPaiionVnuO+5557x9a9/PXbccceCjQ+IGDlyZHzli+fGuw+tiF6VhT8iffr0iYkTJ8YhhxzSrMedffbZ8fa3v71VYa/UAjdt41Of+lSUlytEDAB0XIOresT7dxkV1x6zb/zvG/aMk8YNi17lhflYc11dfdwxc1Gc99/n45TbH4ufPzcjZq/SuhsAAADoHnxDBADtqLS0NE499dSsTdxf//rXuP/++2P9+vVNfvyECRPixBNPjIMPPrio44TurLy8LI7fr0e8YfeK+PcLNfHv59fHrMUtr0YxdOjQ2GOPPWK//fbLlpaEttJ/O1LoK4VGb7jhhnj66aebFRhLVcbS40eN6ljV1AAA8kmh+b0G982WT+8zLu6cuShumjY/nli4oiAHbu7qdXH18zOz5YCh/eK4sUPjjaMGRZ8KH6ECAAAAXVNJfb0a7ADQUaxYsSKeeOKJePbZZ2PmzJmxcOHCWLNmTdTV1UVlZWXWjjJVQNppp51i3333jbFjx7b3kKHLq181K2oev/RVt81bVhfPzayNV+bXxZyldbF4Xf9YtXptrFu3Llvfs2fPrKpg7969Y/jw4dm/2xTSSlUB08+FNmPGjOy/HS+88ELMnTs3+2/J6tWrs2qGaRwprJbGsPvuu2ctctN/SxpSXV0dDb09SP/90coSAOiopq9YEzdPWxC3TJsfC9c2/UScpqgsLYnXjxyUhcgOGd4/a6EJAAAA0FUIjgEAQDODY9sq3+/SKOmtehcAQHuqqauPB+ctzaqQ/Wf2kqgp8PmyA3qUx8QxQ+LYsUNij4F9BOsBAACATk9wDAAA8hAcAwDofJZUr4/bpy+Mm6bOi8nL1xR8+2P6VGUBsmPHDI3RfaoKvn0AAACAtiA4BgAAeQiOAQB0XqkN9wtLV8XfXpkff5+xMFbV1BZ8H3sP7hvHjhkSR48eHAMrKwq+fQAAAIBiERwDAIA8BMcAALqGtTW1cffsxXHT1PnxyILlBd9+WUnEAUP7x5tGD443jBwUA4TIAAAAgA5OcAwAAPKor14ctVOuy3uMysa/K0oqBzmOAACdxOxVa+PmaQvi5qnzY96adUULkb15Y4isvxAZAAAA0AEJjgEAAAAA3VJtfX08Mn9ZVoXsntmLY11dfVFCZAcO7R9vHDU4Xj9iYAzp2aPg+wAAAABoCcExAAAAAKDbW76uJu6ctShum74gnli4omjHY4+BfeLIkQPj9SMGxfh+PaOkpKTbH3sAAACgfQiOAQAAAABs08ry7zMWxm3TFsS0lWuLdmxG9a7MAmSpEtm+Q/pGeWmp5wEAAABoM4JjAAAAAAANqK+vjxeWrsqqkP1jxqJYUr2+aMepb0VZHDisf7xu2IB43fD+MbJ3lecEAAAAKCrBMQAAAACARtTU1cdD85fG7dMXxt2zF0d1bV1Rj9mYPlVxcAqSDR8QBwztF30qyj1HAAAAQEEJjgEAAAAANMOq9bVxz+zFcfv0BfHIgmVRW1/cw1dWErHnoL6x/9B+se/gfrHn4D6CZAAAAECrCY4BAAAAALTQ0ur1WYjsXzMXtUmILCmNiJ0G9I59BveNfYf0i32H9I3BVT2Kv2MAAACgSxEcAwAAAAAoYIjsnzMXxaNtFCLbZHTvqthrcJ/YdUCf2HVg79h5QO/oVV7WdgMAAAAAOh3BMQAAAACAIoTI7p69OAuSPTJ/Wayrq2/bD34jYvu+PbMQ2aYw2S7CZAAAAMBWBMcAAAAAAIpodU1tPDhvafxnzpL475wlsWxdTbsd7xG9KmNc356xQ7+eGy97ZZf9epS325gAAACA9iE4BgAAAADQRmrr6+OpRSviP7MXx7/nLIkZK9d2iGM/uKoiC5Cllpcje1fGiHTZqzK7PqiyIkpKUg0zAAAAoCsRHAMAAAAAaCfTV6yJB+cvyyqSPbpgWayuqetwz0VVWWlWqSyFyLbrVRmDq3rEkKqKGJIue264PrCyIkqFywAAAKBTERwDAAAAAOgAaurq4unFK7MQ2UPzlsVzS1ZGfXQOZSWRVSYbVNUj+vco37ykFpj9e1RsvCyP/pXl0a9iw2XfinJhMwAAAGhHgmMAAJBH/apZUfP4pXmPUfl+l0ZJ71GOIwAABbWsen08smB5VonsyUUrYvKy1Z0mSNYUqfll3xQuqyiLPhXl0WeryxQq69OjLPqUl0ffjZfZzxUpcLbhsndFWZSpcgYAAAAtVt7yhwIAAAAAUCz9KyviTaMHZ0uyfF1NPLVoRTy5aHk8sXBFPL9kZayv67xRsvqNv1NaIqpbtI1e5WUbg2Zl0XtjqKzvxlBZ30bCaOk+laWlUSJ8BgAAQDclOAYAAAAA0Amkdo9HjBiYLUl1bV3WzjKFyVKI7IUlq2LO6pYFsDqr1TW12TJ/TcseX1FasjlcNjC12ty0VG24HLjxMi2Dq3pkYTMAAADoKgTHAAAAAAA6ocqy0thvSL9s2bq95QtLV21YNobJZnezMFlzpIptS6prsmXGyrWN3r93eVkM69kjW4ZuvBzWs3LDZa8eMaJXZRZCAwAAgM7AO1gAAAAAgC7U3vJ1wwdkyybL1q2PKcvWxCsrVscry9fE1BVr4pXlq2PB2vXtOtbOaFVNbbySjt+KNXkrw43sVRkje6elKkaly15V2c8jeldGRWlpm44ZAAAAchEcAwAAAADowvr3qIj9hqZlS2WyZOX6mixIlkJQ01asiVmr1sbsVdUxZ9XaWL6+tt3G29ktX1eTLanq27ZSZCyFx8b26Rlj+1ZtuOxTFWP79syqlpWWlLTLmAEAAOieBMcAAAAAALqh1FJxr8F9s2VbKVSWQmSzN4XJVlfH3NXVsWjt+liwdl12WVtf3y7j7szqImLWqupsuX/eq9dVlpbEmD49Y4d+PWN8v14xoV+v7PqoPlVRJlAGAABAEQiOAQAAAADwmlDZzgPS0rvBI1NXXx9Lq2ti4dp1G5Y16XJ9LF23Pqu2tWzjsun6inU1IWaWX3Vdfby8fHW2RCx6VaBs3MYQ2aZA2fh+PWO7XpUqlAEAANAqgmMAAAAAADRLaqk4qKoiW3aOhsNlW0vVyVIVs2XVNbF84+WmYNnKmppYua42u1yRLtfXxMr1Wy5XrK/t1tXNUqBs0tJV2bK1nmWlMa5fzyxItmP/3rFT/14xoX+vGFhZ0W5jBQAAoHMRHAMAAAAAoKhSq8X+PSqypbnq6+ujurYuC5CtWF8TqzZevjpc9urw2aqa2qzK2cqa2li5ribW1KYmkV1L+p2eX7IqWyIWbL59cFVF7JiFyTYEytLluL49o0dZabuOFwAAgI5HcAwAAAAAgA6rpKQkqsrLsmVozx4t2kZNXd3GwNmrK5pt+jlVP1u8dn0srt6wLNl4fW0nDJwtWrs+Fq1dFg/OX/aq4N64vlWbg2SblqFVPbLjCwAAQPckOAYAAAAAQJdWXloa/SvT0ryKZ6trarMQ2aLq9bFgzbqYv6Y65meXG5YNt63r8K000/gmL1+TLX+fseX2fj3KN4TI+vXKWl2mYNn4fj2zkB4AAABdn+AYAAAAAAA0oFd5WfTqUxaj+lTlPD519fWxpHp9zF5VHbNXV8fsVWs3XN94OW9NddR20FzZ8nU18diC5dmySao/NrpP1eaqZDv121ClbETvyihVnQwAAKBLERwDAAAAAIAWSmGqwVU9smWvwX1fs76mrj6rVDZz5dqYni1rYvqKDZdzVlVHR2uGmTJuM1auzZa7Zi3efHuv8tKY0K/Xa9pd9qnwNQMAAEBn5R0dAAAAAAAUSXlpSYzsXZUtBw9/9bp1tXUxa9WGQNm0FWtiyvLVMWX5mpi6fHVU13WsMmWra+ri6cUrs2VrI3pVZoGy1OJybN+eMa5vz9i+b8+sDSYAAAAdm3duAAAAAADQDnqUlcYO/Xply9Zq6+uzVpcpRLYhTLYhUJbCZes7WKBszurqbPnv3CWvun1gZXkWINu+z4Yg2dg+VVnLz5G9K6OqrKzdxgsAAMAWgmMAAAAAANCBlJWUxJg+PbPlqJGDXtX2MrW8nLJidUxZtjomL18dLy9bnbWV7Fhxsogl1TWxpHpFPLFwxWvWDamqiFG9qzYulVk1tnQ5vFdlDKnqkVVpAwAAoPgExwAAAAAAoBNIgapx/Xpmy9GjBm++fU1NbbyyfE28vGxVvLRsdbycAmVLV8Xy9bXRES1cuz5bnlz02lBZaUQMrqqIYT0rY1ivHjGsZ48Ynq737JGFygZWVmTVzPr2KI/SEgEzAACA1hAcAwAAAACATqxneVnsPqhPtmxSX18fC9auyyqSbVlWxdQVa7NWmB1VXUQsWLs+W559dffLVykriRiQhcgqYtDGy/49NgTK+laURZ+KLZd9Ksqi78bLdKwqSkuiROgMAABAcAwAoLtbu3ZtTJo0KV555ZVsmT59eqxZsyZqamqivLw8evbsGWPHjo0ddtghW3bZZZeoqqpq72EDAACQRwpGZVW7elbGYdsN3Hz7utq6mLpizeYgWXa5fHUsWru+Ux3P2vrIxtyScaeqZlXlpVFZVhZVZaUblvINlxWlpVmr0FTdraHLV1+PKNvUVrN+y0X9VuG9rVZtVleflvrs9nS59c8p1JceVhcbLpvz86Ztbdlu03/esJ36LLi3eTzb/rzx2KVKb+nX3nC51fWN69JxSa+/TceovLQ0epSWZMc2HbseGy8rNt5WsfX1spKozJ6TbZ+bDT9XbvVcbb5P+YbnDQAAaL6S+k3vXAAA6FZSQOyOO+6I//73v1FdXd3kx1VWVsYRRxwREydOzAJlXV39qllR8/ilee9Tvt+lUdJ7VJuNCQAAoNCWVK+PyctWb2h1uTFQNmX56liXUkPQwaVgWq/ysuhdURa9N15u+bl8y8+bbtv25/IN1el6lZeqRgcAQLciOAYA0M3MmDEjrrnmmnjuuedava3dd989zjjjjBgzZkx0VYJjAABAd1VTVx8zV66Nl5dvrEy2cZmzuuknH0FnkuqWpZamvTe2Nt2wlDd4mdqfptDZ1q1Q08+VpcJnAAB0HoJjAADdRG1tbdx0001xww03ZG0oCyW1szz11FPjxBNPjLKysuhqBMcAAABebcW6mpi8fEuQbNqKNVn7y8XVnavdJRRDeUlJ9O2xodJZ7oDZpnUbgmi9t1qXltTeEwAA2oLgGABAN7BkyZL43ve+F5MnTy7aPiZMmBDnn39+DBw4MLoSwTEAAICmB8qmr1wT01as3RwmSz/PWLk21mt5CU1WVVa6TZWzjQGz8rLo22Pjbam9Zrq+sc1mnx7ptg3tNqvKy7L2nSUlJY46AAB5CY4BAHRxCxYsiMsvvzzmzZtX9H0NHz48Lrzwwhg6dGh0FYJjAAAArVNXXx8L1qyL2auqY+aqtTFr1drserpMy5LqwlXFBjZINctSgKxneWn0LNsQJkuXPcvLsmDa1pfpPlVlW+5bWVYaPdJSuuH6lp9LtvxcuuU2ATUAgM5LcAwAoItXGvvqV7/aJqGxrcNjl1xySZepPCY4BgAAUFyr1tfG/DXVMX/Nupi3Zt2G66vT5cbra9bFivW1ngbooCpLS7IQ2daBsi0Bsw3r0u3lpSVRkS2lr7osb+C2Tddf+5gtt/fY5vHpsqykZPPlhiUE2wAA8ijPtxIAgM6rtrY2a0/ZlqGxJO0v7ffSSy+NsrKyNt03AAAAnU/virLYoaJX7NCvV877rK2pzSqTLaleH4ur12eXWy+L166PletrY8X6mixktnJ9jfaY0Eaq6+qjuq62wwY8tw6TlZdElKWQWXaZft4YMNt0fZvwWb7bNj12c1AtzzbS9Wx5zfU0lo333Wb9ax9b+prtlGpHCgC0kuAYAEAXddNNN8XkyZPbZd9pvzfffHOcfPLJ7bJ/AAAAupbUZm9EWnpXNun+9fUpyFKXVTNbsW5DoCxdr66ti7W1tbE2u9ywrKn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" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1223 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "pc_mu = az.plot_dist(\n", + " idata_partial_bern,\n", + " var_names=[\"mu\"],\n", + " visuals={\"title\": {\"text\": r\"Population log-odds effect $\\mu$\"}},\n", + ")\n", + "az.add_lines(\n", + " pc_mu,\n", + " values=TRUE_MU_LOGIT,\n", + " visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_MU_LOGIT:.2f}\"}},\n", + ")\n", + "pc_mu.get_viz(\"plot\").legend()\n", + "\n", + "pc_tau = az.plot_dist(\n", + " idata_partial_bern,\n", + " var_names=[\"tau\"],\n", + " visuals={\"title\": {\"text\": r\"Between-market SD $\\tau$ (log-odds)\"}},\n", + ")\n", + "az.add_lines(\n", + " pc_tau,\n", + " values=TRUE_TAU_LOGIT,\n", + " visuals={\"ref_line\": {\"color\": \"C2\", \"label\": f\"true = {TRUE_TAU_LOGIT:.2f}\"}},\n", + ")\n", + "pc_tau.get_viz(\"plot\").legend();" + ] + }, + { + "cell_type": "markdown", + "id": "355a8d07", + "metadata": {}, + "source": [ + "The Bernoulli picture is the Gaussian picture on a different link. The population mean log-odds effect is recovered; the between-market variance is recovered; the per-market shrinkage works as before. The log-odds parameterisation carries a structural advantage the probability scale does not: a given value of τ means the same degree of between-market variability in the treatment effect regardless of what the baseline conversion rate happens to be. On the probability scale, a τ of 0.05 is meaningful heterogeneity at a 5\\% baseline and negligible noise at a 50\\% baseline; on the logit, τ is scale-invariant in the way the analysis needs it to be." + ] + }, + { + "cell_type": "markdown", + "id": "d4c871ab", + "metadata": {}, + "source": [ + "## How much to borrow\n", + "\n", + "With $\\tau$ estimated on both scales, borrowing across markets raises a question the hierarchical model answers quietly: how far should one market's estimate move toward the others. The shrinkage already shown is that answer in action. Each market's pull toward the population mean is a weight set by its own precision against the between-market variance $\\tau$ the data infer." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "4c87404e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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marketseweight_on_population_mean
0Market A0.4230.466
1Market B0.3590.385
2Market C0.3300.347
3Market D0.2960.300
4Market E0.2770.272
5Market F0.2550.241
6Market G0.2120.180
7Market H0.1630.115
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" + ], + "text/plain": [ + " market se weight_on_population_mean\n", + "0 Market A 0.423 0.466\n", + "1 Market B 0.359 0.385\n", + "2 Market C 0.330 0.347\n", + "3 Market D 0.296 0.300\n", + "4 Market E 0.277 0.272\n", + "5 Market F 0.255 0.241\n", + "6 Market G 0.212 0.180\n", + "7 Market H 0.163 0.115" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tau_post_mean = float(idata_partial.posterior[\"tau\"].mean())\n", + "shrinkage_weight = se_obs**2 / (se_obs**2 + tau_post_mean**2)\n", + "borrow_df = pd.DataFrame(\n", + " {\n", + " \"market\": MARKET_NAMES,\n", + " \"se\": se_obs,\n", + " \"weight_on_population_mean\": shrinkage_weight,\n", + " }\n", + ").round(3)\n", + "borrow_df" + ] + }, + { + "cell_type": "markdown", + "id": "5511e1fd", + "metadata": {}, + "source": [ + "Noisy markets carry the largest weight on the population mean, so they borrow the most; precise markets keep their own estimate. The between-market variance sets the scale, and the data set $\\tau$, so the borrowing rate adapts to the evidence. This is the dynamic borrowing the FDA guidance describes, where the amount borrowed responds to the similarity among the sources {cite:p}`fda2026bayesian`.\n", + "\n", + "Borrowing earns its keep through precision: a prior built from real past experiments sharpens the next posterior and lowers the sample size needed to reach a given assurance, so the eight markets already run are information the ninth should use. The open question is how much of it to grant, and a *power prior* makes that dial explicit {cite:p}`ibrahim2000power`. Raise the pooled likelihood from the past markets to a discount $\\alpha$ in the unit interval and use the result as the prior for the new market. With $n_0$ past subjects it contributes about $\\alpha\\, n_0$ observations' worth of information, so $\\alpha$ is the fraction of the historical sample size carried forward, the prior effective sample size {ref}`assurance_planning` planned around. At $\\alpha = 1$ the past markets count in full, as if pooled; as $\\alpha$ falls toward zero the prior widens and the borrowing fades. Fixing $\\alpha$ in advance is what makes the power prior the static counterpart to the hierarchical model's data-driven $\\tau$.\n", + "\n", + "The word *power* here means raising the likelihood to an exponent, a separate idea from the statistical power and assurance of {ref}`assurance_planning`. The two meet only through effective sample size: $\\alpha$ sets how many past observations the prior is worth, and that count is the quantity the planning notebook traded against sample size." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "5915e805", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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alphaprior_meanprior_sd
00.100.3080.286
10.250.3080.181
20.500.3080.128
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" + ], + "text/plain": [ + " alpha prior_mean prior_sd\n", + "0 0.10 0.308 0.286\n", + "1 0.25 0.308 0.181\n", + "2 0.50 0.308 0.128\n", + "3 0.75 0.308 0.105\n", + "4 1.00 0.308 0.091" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "w_pool = 1.0 / se_obs**2\n", + "pooled_mean = float(np.sum(w_pool * d_hat_obs) / np.sum(w_pool))\n", + "pooled_var = float(1.0 / np.sum(w_pool))\n", + "\n", + "alpha_grid = np.array([0.1, 0.25, 0.5, 0.75, 1.0])\n", + "power_prior_df = pd.DataFrame(\n", + " {\"alpha\": alpha_grid, \"prior_mean\": pooled_mean, \"prior_sd\": np.sqrt(pooled_var / alpha_grid)}\n", + ").round(3)\n", + "power_prior_df" + ] + }, + { + "cell_type": "markdown", + "id": "bb991411", + "metadata": {}, + "source": [ + "The power prior must be measured against the belief the hierarchical model already holds about a market it has not seen. That belief is the model's *predictive distribution*, and it comes in two forms. The true-effect predictive gives the unknown effect of a new market drawn from the same population,\n", + "\n", + "$$\\theta_{\\text{new}} \\mid \\text{data} \\sim \\mathcal{N}\\!\\left(\\mu_{\\text{post}},\\ \\sqrt{\\tau_{\\text{post}}^2 + \\sigma_{\\mu,\\text{post}}^2}\\right),$$\n", + "\n", + "and the observation predictive layers experimental noise on top,\n", + "\n", + "$$\\hat d_{\\text{new}} \\mid \\text{data} \\sim \\theta_{\\text{new}} + \\mathcal{N}(0, s_{\\text{new}}).$$\n", + "\n", + "We draw both now. The first sets the width the power prior is chasing; the second is the yardstick for the conflict check below. The power prior borrows the precision of the pooled mean and treats every market as one draw from a single shared effect, while the hierarchical predictive folds the between-market variation back in through $\\tau$. The figure sets the two side by side." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "91ce8350", + "metadata": {}, + "outputs": [], + "source": [ + "mu_samples = idata_partial.posterior[\"mu\"].values.flatten()\n", + "tau_samples = idata_partial.posterior[\"tau\"].values.flatten()\n", + "rng_pp = np.random.default_rng(RANDOM_SEED + 1)\n", + "theta_new_samples = rng_pp.normal(mu_samples, tau_samples)\n", + "s_new = np.median(se_obs)\n", + "d_hat_new_samples = theta_new_samples + rng_pp.normal(0.0, s_new, size=len(theta_new_samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "de589904", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 923, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "theta_new_mean = float(theta_new_samples.mean())\n", + "theta_new_sd = float(theta_new_samples.std())\n", + "alpha_match = (\n", + " pooled_var / theta_new_sd**2\n", + ") # discount at which the power prior reaches the tau-driven width\n", + "xx = np.linspace(pooled_mean - 1.2, pooled_mean + 1.2, 400)\n", + "\n", + "fig, ax = plt.subplots(figsize=(20, 4.5))\n", + "for a in [1.0, 0.5, 0.1]:\n", + " sd_a = np.sqrt(pooled_var / a)\n", + " ax.plot(xx, stats.norm.pdf(xx, pooled_mean, sd_a), label=rf\"Power prior, $\\alpha$ = {a}\")\n", + "ax.plot(\n", + " xx,\n", + " stats.norm.pdf(xx, pooled_mean, np.sqrt(pooled_var / alpha_match)),\n", + " color=\"C1\",\n", + " linestyle=\"--\",\n", + " label=rf\"Power prior matching $\\tau$ ($\\alpha \\approx$ {alpha_match:.2f})\",\n", + ")\n", + "ax.plot(\n", + " xx,\n", + " stats.norm.pdf(xx, theta_new_mean, theta_new_sd),\n", + " color=\"black\",\n", + " linewidth=2.5,\n", + " label=r\"Hierarchical predictive ($\\tau$-driven)\",\n", + ")\n", + "ax.axvline(0.0, color=\"grey\", linestyle=\":\", alpha=0.6)\n", + "ax.set_xlabel(r\"Effect in a new market $\\theta_{\\text{new}}$\")\n", + "ax.set_ylabel(\"Prior density\")\n", + "ax.set_title(\"Static power prior versus dynamic hierarchical borrowing\")\n", + "ax.legend();" + ] + }, + { + "cell_type": "markdown", + "id": "d91959be", + "metadata": {}, + "source": [ + "At $\\alpha = 1$ the static power prior is the tightest curve, far more confident about a new market than the spread across markets warrants. Matching the hierarchical predictive takes a large deviation from full borrowing: the dashed curve marks the small $\\alpha$ at which the static prior finally reaches the $\\tau$-driven width, and that value has to be set by hand. The hierarchical model arrives there on its own, because $\\tau$ reads the between-market spread from the data.\n", + "\n", + "Either prior becomes the belief the next market inherits, and that inheritance is legitimate only when the new market is drawn from the same population the past markets describe. Borrowing sharpens the posterior when that holds and pulls it toward the wrong centre when it fails, so the strength of borrowing has to be earned rather than assumed. A prior-data conflict check is the gate {cite:p}`evans2006checking`: locate the incoming estimate in the prior predictive distribution, and read a small tail probability as the new market disagreeing with the borrowed belief." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "b0b7bf16", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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incoming estimateprior-predictive tail probability
concordant market0.280.796
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" + ], + "text/plain": [ + " incoming estimate prior-predictive tail probability\n", + "concordant market 0.28 0.796\n", + "conflicting market -1.00 0.028" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def prior_data_conflict_tail(d_new, prior_pred_samples):\n", + " centre = np.median(prior_pred_samples)\n", + " return float(np.mean(np.abs(prior_pred_samples - centre) >= abs(d_new - centre)))\n", + "\n", + "\n", + "concordant_d_new = 0.28 # a new market in line with the population\n", + "conflicting_d_new = -1.0 # a new market that contradicts the population\n", + "pd.DataFrame(\n", + " {\n", + " \"incoming estimate\": [concordant_d_new, conflicting_d_new],\n", + " \"prior-predictive tail probability\": [\n", + " prior_data_conflict_tail(concordant_d_new, d_hat_new_samples),\n", + " prior_data_conflict_tail(conflicting_d_new, d_hat_new_samples),\n", + " ],\n", + " },\n", + " index=[\"concordant market\", \"conflicting market\"],\n", + ").round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "690ea5aa", + "metadata": {}, + "source": [ + "The concordant market sits in the body of the predictive and the tail probability is large; the prior and the new data describe one population, so the experiment can borrow at full strength and keep the precision that buys. The conflicting market sits far out and the tail probability is small, the trigger the guidance names for reassessing how much to borrow {cite:p}`fda2026bayesian`: lower $\\alpha$, widen the prior, or hold the borrowed estimate aside until the discrepancy is understood. Dynamic borrowing through $\\tau$ softens this failure on its own, since a heterogeneous set of markets produces a wide predictive that absorbs a surprising estimate, while a static power prior never adapts, so the analyst must run the check every time. Whatever borrowing strength passes the check is the prior the next experiment plans with." + ] + }, + { + "cell_type": "markdown", + "id": "469f684d", + "metadata": {}, + "source": [ + "## Predicting the next experiment\n", + "\n", + "The predictive we drew to calibrate borrowing also answers the question that occasioned the whole exercise: what will happen if we run the redesign in a market we have not tested yet. The two flavours now do decision work. The true-effect predictive $\\theta_{\\text{new}}$ is the best estimate of the effect in a new market; the observation predictive $\\hat d_{\\text{new}}$ is what to expect the next experiment to actually return, noise included. The gap between them is the experimental-noise envelope that a single-market estimate conflates with population variation." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "1a090549", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 1448 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "dt = az.from_dict(\n", + " {\n", + " \"posterior\": {\n", + " \"theta_new\": theta_new_samples,\n", + " \"d_hat_new\": d_hat_new_samples,\n", + " }\n", + " },\n", + " sample_dims=[\"sample\"],\n", + ")\n", + "\n", + "pc = az.plot_dist(\n", + " dt,\n", + " kind=\"hist\",\n", + " sample_dims=[\"sample\"],\n", + " cols=[],\n", + " aes={\"color\": [\"__variable__\"]},\n", + " visuals={\n", + " \"point_estimate\": False,\n", + " \"point_estimate_text\": False,\n", + " \"credible_interval\": False,\n", + " \"title\": {\"text\": \"Two predictive distributions for the ninth market\"},\n", + " },\n", + ")\n", + "pc.add_legend(\"__variable__\")\n", + "az.add_lines(pc, values=0.0, visuals={\"ref_line\": {\"color\": \"black\", \"label\": \"0\"}});" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "645d5c5e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:37.779232Z", + "iopub.status.busy": "2026-06-01T17:59:37.779104Z", + "iopub.status.idle": "2026-06-01T17:59:37.783309Z", + "shell.execute_reply": "2026-06-01T17:59:37.782922Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
posterior probability > 0
$\\theta_{\\text{new}}$ (true effect)0.825
$\\hat d_{\\text{new}}$ (observed estimate)0.784
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" + ], + "text/plain": [ + " posterior probability > 0\n", + "$\\theta_{\\text{new}}$ (true effect) 0.825\n", + "$\\hat d_{\\text{new}}$ (observed estimate) 0.784" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prob_theta_new_positive = float((theta_new_samples > 0).mean())\n", + "prob_d_hat_new_positive = float((d_hat_new_samples > 0).mean())\n", + "pd.DataFrame(\n", + " {\"posterior probability > 0\": [prob_theta_new_positive, prob_d_hat_new_positive]},\n", + " index=[r\"$\\theta_{\\text{new}}$ (true effect)\", r\"$\\hat d_{\\text{new}}$ (observed estimate)\"],\n", + ").round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "cb419ca8", + "metadata": {}, + "source": [ + "The probability the true effect is positive in the next market is higher than the probability the next experiment will return a positive estimate. The gap is the experimental-noise tax: each individual experiment is a noisy realisation of an underlying truth, and the team will sometimes see a negative estimate even when the true effect is positive. Reporting the meta-analytic posterior on $\\theta_{\\text{new}}$ as the planning input for the next market, which {ref}`assurance_planning` then consumes as its prior, is the way to feed accumulating evidence forward without losing track of the noise." + ] + }, + { + "cell_type": "markdown", + "id": "c9a8d6b4", + "metadata": {}, + "source": [ + "## The synthesis becomes the next plan\n", + "\n", + "The predictive that calibrated borrowing also answers the question the planning notebook opens with. Read off its centre and width and the loop is closed explicitly: this synthesis is the prior {ref}`assurance_planning` integrates over." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "8be48397", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " value\n", + "planning prior mean μ 0.400\n", + "planning prior sd σ 0.500\n", + "assurance ceiling P(θ_new > 0) 0.788" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The true-effect predictive is exactly what the planning notebook treats as its\n", + "# prior: a Normal summarised by a location and a width.\n", + "planning_mu = round(float(theta_new_mean), 1)\n", + "planning_sigma = round(float(theta_new_sd), 1)\n", + "assurance_ceiling_next = 1.0 - stats.norm.cdf(0.0, planning_mu, planning_sigma)\n", + "\n", + "pd.DataFrame(\n", + " {\"value\": [planning_mu, planning_sigma, round(float(assurance_ceiling_next), 3)]},\n", + " index=[\n", + " \"planning prior mean μ\",\n", + " \"planning prior sd σ\",\n", + " \"assurance ceiling P(θ_new > 0)\",\n", + " ],\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "93470378", + "metadata": {}, + "source": [ + "`EffectPrior(mu=planning_mu, sigma=planning_sigma)` is the object {ref}`assurance_planning` opens with." + ] + }, + { + "cell_type": "markdown", + "id": "e7c2c1c7", + "metadata": {}, + "source": [ + "## Replication as the data-generating process\n", + "\n", + "A single experiment is overheard speech. Eight experiments are conversation. The hierarchical model is what lets us hear them as conversation, and the posterior on the population describes the very population our experiments were drawn from.\n", + "\n", + "Replication is often described as a verification protocol, a post-hoc check on a result already in hand. It is better understood as the data-generating process whose distribution we are trying to learn. Each new market is a draw from a population we never observed directly; pooling constructs that population from the draws; the next experiment tests whether the constructed population keeps predicting new markets. The three notebooks make the same move on three problems. Planning became a posterior over the posteriors a future experiment will compute. Interpretation became a posterior over the bias a single experiment cannot rule out. Synthesis became a posterior over the population a series of experiments samples from. The likelihood changed from Gaussian to Bernoulli each time and the picture held. In each, an assumption a conventional analysis leaves implicit is made a parameter with a posterior, something to argue about rather than assume. The problem changes; its proper characterisation is always a posterior.\n", + "\n", + "And the last question feeds the first. The population this notebook inferred is the prior the planning notebook consumes: $\\theta_{\\text{new}} \\sim \\mathcal{N}(\\mu, \\tau)$ is the kind of belief {ref}`assurance_planning` integrates over before the next experiment is run. The synthesis that ends one experiment's lifecycle is the input to the design of the next. The lifecycle runs as a loop rather than a line from plan to verdict, and the posterior is what travels around it: each notebook's synthesis becomes the next notebook's prior, and each overheard conversation becomes the next one's opening question.\n", + "\n", + "## Authors\n", + "\n", + "- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026.\n", + "\n", + "## References\n", + "\n", + ":::{bibliography}\n", + ":filter: docname in docnames\n", + ":::\n", + "\n", + "## Watermark" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "2e2e3295", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-01T17:59:37.784599Z", + "iopub.status.busy": "2026-06-01T17:59:37.784526Z", + "iopub.status.idle": "2026-06-01T17:59:37.795615Z", + "shell.execute_reply": "2026-06-01T17:59:37.795126Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last updated: Mon, 29 Jun 2026\n", + "\n", + "Python implementation: CPython\n", + "Python version : 3.13.13\n", + "IPython version : 9.14.0\n", + "\n", + "pytensor: 3.0.3\n", + "xarray : 2026.4.0\n", + "\n", + "arviz : 1.1.0\n", + "matplotlib: 3.10.9\n", + "numpy : 2.3.5\n", + "pandas : 2.3.3\n", + "pymc : 6.0.1\n", + "scipy : 1.17.1\n", + "\n", + "Watermark: 2.6.0\n", + "\n" + ] + } + ], + "source": [ + "%load_ext watermark\n", + "%watermark -n -u -v -iv -w -p pytensor,xarray" + ] + }, + { + "cell_type": "markdown", + "id": "964065d7", + "metadata": {}, + "source": [ + ":::{include} ../page_footer.md\n", + ":::" + ] + } + ], + "metadata": { + "jupytext": { + "default_lexer": "ipython3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/causal_inference/multiple_experiments_meta_analysis.myst.md b/examples/causal_inference/multiple_experiments_meta_analysis.myst.md new file mode 100644 index 000000000..163699a87 --- /dev/null +++ b/examples/causal_inference/multiple_experiments_meta_analysis.myst.md @@ -0,0 +1,773 @@ +--- +jupytext: + default_lexer: ipython3 + text_representation: + extension: .md + format_name: myst + format_version: 0.13 +kernelspec: + display_name: Python 3 + language: python + name: python3 +--- + +(meta_analysis_experiments)= +# Multiple Experiments and Bayesian Meta-analysis + +:::{post} May 2026 +:tags: experimentation, meta-analysis, hierarchical models, partial pooling, replication +:category: intermediate, reference +:author: Nathaniel Forde +::: + +:::{figure} experimentation_triptych.jpeg +:name: experimentation-triptych +:width: 100% +:align: center + +The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance:* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis:* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis (this notebook):* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery. +::: + +## The replication-as-evidence problem + +Eight quarterly A/B tests of the same checkout-flow redesign, run across eight markets, return eight different point estimates. Two cross the conventional significance threshold; the other six do not. The product manager asks the natural question, "did it work?", and gets two incompatible defaults depending on which colleague answers: vote-counting ("four out of eight worked, so it's a wash"), or pool-everything ("the combined estimate is positive, so it works"). Both are mistakes. The vote-count discards the magnitude information in each estimate; the pool-everything pretends the markets are exchangeable in a way the evidence does not support. The honest answer requires a model that estimates between-market differences rather than assuming them away. + +Each experiment speaks about one market. The hierarchy is what lets us hear all of them at once. + +This notebook builds that model. The hierarchical Bayesian meta-analysis treats each experiment as a noisy estimate of its own market's true effect, and treats the per-market effects as draws from a population whose mean and variance are themselves the quantities of substantive interest {cite:p}`borenstein2009meta`, {cite:p}`higgins2009meta`. The structure is the one Rubin used for the 8-schools problem in 1981 {cite:p}`rubin1981estimation`, {cite:p}`gelman2013bayesian`, transposed to product experimentation. We develop it on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the third of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`sensitivity_confounding` for the interpretation counterpart. Readers wanting a deeper view of the partial-pooling vocabulary should also consult the existing PyMC notebooks on {ref}`multilevel_modeling` and {ref}`hierarchical_partial_pooling`, which we treat as predecessors rather than re-derive. + +:::{admonition} Where this lands in regulatory practice +:class: note + +The hierarchical model here is the borrowing mechanism a regulator now describes by name. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials presents subgroup analysis through a *one-way Bayesian hierarchical model* whose subgroup estimate is "a weighted average of its raw estimated treatment effect ... and the overall estimated treatment effect" {cite:p}`fda2026bayesian`, the shrinkage picture this notebook builds. The same guidance treats hierarchical models as the main way to borrow information across related trials by assuming the group parameters are drawn from a common distribution, which is the $\theta_k \sim \mathcal{N}(\mu, \tau)$ structure below. Borrowing across studies, and the use of one trial's synthesis as the next trial's prior, is the regulatory form of the lifecycle loop these three notebooks trace. +::: + +```{code-cell} ipython3 +import warnings + +import arviz as az +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +import pymc as pm + +from scipy import stats + +warnings.filterwarnings("ignore", category=RuntimeWarning) +warnings.filterwarnings("ignore", category=UserWarning) +``` + +```{code-cell} ipython3 +%config InlineBackend.figure_format = 'retina' +az.style.use("arviz-variat") +rng = np.random.default_rng(11) +RANDOM_SEED = 11 +``` + +## Heterogeneity is not new: groups within a single study + +The across-study problem looks novel, but its structure appears inside a single experiment whenever the treatment effect varies across user segments. It is worth meeting the problem on this familiar ground first, because the tool that solves it here is the tool we will carry across studies, and its classical name is the analysis of variance. + +Consider one market's experiment broken out across six user segments. The redesign helps some segments more than others, and the per-segment treatment effects are themselves draws from a population. We give the section its own random generator so the across-study results later in the notebook are unaffected. + +```{code-cell} ipython3 +seg_rng = np.random.default_rng(2024) + +SEG_NAMES = [ + "New / mobile", + "New / desktop", + "Returning / mobile", + "Returning / desktop", + "High-value", + "Reactivated", +] +N_PER_SEGMENT = np.array([600, 600, 900, 900, 1400, 1400]) # visitors per segment +SEG_MU, SEG_TAU = 0.30, 0.50 +BASELINE, SIGMA_OBS = 10.0, 4.0 + + +def simulate_within_study_segments(seg_names, N_per_seg, seg_mu, seg_tau, baseline, sigma_obs, rng): + true_effects = rng.normal(seg_mu, seg_tau, size=len(seg_names)) + rows = [] + for name, N_seg, eff in zip(seg_names, N_per_seg, true_effects): + treat = rng.integers(0, 2, size=int(N_seg)) + revenue = baseline + eff * treat + rng.normal(0, sigma_obs, size=int(N_seg)) + rows.append(pd.DataFrame({"segment": name, "treatment": treat, "revenue": revenue})) + return pd.concat(rows, ignore_index=True), true_effects + + +study_df, seg_true_effects = simulate_within_study_segments( + SEG_NAMES, N_PER_SEGMENT, SEG_MU, SEG_TAU, BASELINE, SIGMA_OBS, seg_rng +) +study_df.head() +``` + +The per-segment treatment effect is a difference of arm means; its standard error follows from the within-arm variances. + +```{code-cell} ipython3 +def segment_effect_estimates(df): + recs = [] + for name, g in df.groupby("segment", sort=False): + t = g.loc[g.treatment == 1, "revenue"] + c = g.loc[g.treatment == 0, "revenue"] + recs.append( + { + "segment": name, + "d": t.mean() - c.mean(), + "se": np.sqrt(t.var(ddof=1) / len(t) + c.var(ddof=1) / len(c)), + } + ) + return pd.DataFrame(recs) + + +seg_est = segment_effect_estimates(study_df) +seg_est.round(3) +``` + +The classical question "does the effect differ across segments?" is a test for the treatment-by-segment interaction, and the two-way analysis of variance answers it with an $F$-test. We compute it directly, as a comparison of nested least-squares fits, which keeps the dependency surface small and makes the variance decomposition explicit. The interaction row is the one to read. + +```{code-cell} ipython3 +def anova_two_way(df, outcome, factor, treatment): + """Type-II two-way ANOVA via nested least-squares fits (treatment is binary).""" + y = df[outcome].to_numpy(dtype=float) + n = len(y) + ones = np.ones((n, 1)) + A = pd.get_dummies(df[factor], drop_first=True).to_numpy(dtype=float) # factor dummies + B = pd.get_dummies(df[treatment], drop_first=True).to_numpy(dtype=float) # treatment dummy + AB = A * B # interaction columns + + def fit(*blocks): + X = np.hstack([ones, *blocks]) + beta, *_ = np.linalg.lstsq(X, y, rcond=None) + resid = y - X @ beta + return float(resid @ resid), np.linalg.matrix_rank(X) + + rss_full, k_full = fit(A, B, AB) + rss_add, k_add = fit(A, B) + rss_A, k_A = fit(A) + rss_B, k_B = fit(B) + df_resid = n - k_full + mse = rss_full / df_resid + + terms = { + f"C({factor})": (rss_B - rss_add, k_add - k_B), + f"C({treatment})": (rss_A - rss_add, k_add - k_A), + f"C({factor}):C({treatment})": (rss_add - rss_full, k_full - k_add), + } + rows = [ + { + "sum_sq": ss, + "df": float(dof), + "F": (ss / dof) / mse, + "PR(>F)": stats.f.sf((ss / dof) / mse, dof, df_resid), + } + for ss, dof in terms.values() + ] + rows.append({"sum_sq": rss_full, "df": float(df_resid), "F": np.nan, "PR(>F)": np.nan}) + return pd.DataFrame(rows, index=list(terms) + ["Residual"]) + + +anova_tbl = anova_two_way(study_df, "revenue", "segment", "treatment") +anova_tbl.round(3) +``` + +The interaction $F$-test reports whether heterogeneity is detectable; it does not estimate how large it is. + +:::{admonition} Three numbers for heterogeneity +:class: note + +Given per-group effect estimates $\hat d_k$ with standard errors $s_k$ and inverse-variance weights $w_k = 1/s_k^2$: + +- **Cochran's $Q$** measures how far the estimates spread beyond what sampling noise alone would produce. It is $Q = \sum_k w_k (\hat d_k - \bar d)^2$, where $\bar d$ is the precision-weighted mean, and it is simply the inverse-variance-weighted version of the between-groups sum of squares from ANOVA. If every group shared one true effect, $Q$ would follow a $\chi^2$ distribution with $K-1$ degrees of freedom, so a $Q$ much larger than $K-1$ is evidence of real heterogeneity. +- **$I^2 = \max\!\big(0,\, (Q - (K-1))/Q\big)$** rescales $Q$ onto the unit interval: the share of the total variation in the estimates due to genuine between-group differences rather than sampling error. $I^2 = 0$ means the spread is all noise; $I^2 = 0.9$ means most of it is real. +- **The DerSimonian–Laird estimator** is the classical, non-Bayesian way to turn $Q$ into a point estimate of the between-group variance $\tau^2$. It is a method-of-moments calculation, and once $\hat\tau^2$ is in hand the random-effects pooled mean re-weights each group by $1/(s_k^2 + \hat\tau^2)$ instead of $1/s_k^2$, so noisy groups count for less and no single precise group dominates. + +See {cite:p}`borenstein2009meta` for the full treatment and {cite:p}`higgins2009meta` for the random-effects model these statistics serve. +::: + +```{code-cell} ipython3 +d = seg_est["d"].values +s = seg_est["se"].values +w = 1.0 / s**2 +d_fixed = np.sum(w * d) / np.sum(w) +se_fixed = np.sqrt(1.0 / np.sum(w)) +df_q = len(d) - 1 +Q = np.sum(w * (d - d_fixed) ** 2) +p_Q = stats.chi2.sf(Q, df_q) +I2 = max(0.0, (Q - df_q) / Q) +C_dl = np.sum(w) - np.sum(w**2) / np.sum(w) +tau2_DL = max(0.0, (Q - df_q) / C_dl) +w_re = 1.0 / (s**2 + tau2_DL) +mu_DL = np.sum(w_re * d) / np.sum(w_re) +se_DL = np.sqrt(1.0 / np.sum(w_re)) + +print(f"Cochran's Q = {Q:.2f} (df = {df_q}, p = {p_Q:.3f})") +print(f"I² = {I2:.2f} DerSimonian–Laird between-segment SD τ = {np.sqrt(tau2_DL):.3f}") +``` + +The hierarchical Bayesian model is the same random-effects analysis of variance, with one difference that matters when the number of groups is small: it returns a posterior over $\tau$ rather than a single number. With only six segments $\tau$ is weakly identified, and the DerSimonian–Laird point estimate can collapse toward zero even when real heterogeneity is present; the posterior shows that uncertainty honestly instead of hiding it in a point. + +```{code-cell} ipython3 +coords_seg = {"segment": SEG_NAMES} +with pm.Model(coords=coords_seg) as segment_model: + mu = pm.Normal("mu", mu=0.0, sigma=1.0) + tau = pm.HalfNormal("tau", sigma=1.0) + offset = pm.Normal("offset", mu=0.0, sigma=1.0, dims="segment") + theta = pm.Deterministic("theta", mu + tau * offset, dims="segment") + pm.Normal("d_obs", mu=theta, sigma=s, observed=d, dims="segment") + idata_seg = pm.sample( + draws=2000, + tune=2000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) +``` + +```{code-cell} ipython3 +mu_post = idata_seg.posterior["mu"] +tau_post = idata_seg.posterior["tau"] +comparison = pd.DataFrame( + { + "pooled effect": [d_fixed, mu_DL, float(mu_post.mean())], + "se / sd": [se_fixed, se_DL, float(mu_post.std())], + "between-segment τ": [0.0, np.sqrt(tau2_DL), float(tau_post.mean())], + }, + index=[ + "Fixed-effect ANOVA (complete pooling)", + "Random-effects ANOVA (DerSimonian–Laird)", + "Hierarchical Bayes (partial pooling)", + ], +) +comparison.round(3) +``` + +```{code-cell} ipython3 +pc = az.plot_dist( + idata_seg, + var_names=["tau"], + visuals={ + "title": {"text": r"Posterior of between-segment SD $\tau$ (one study, six segments)"} + }, +) +az.add_lines( + pc, + values=np.sqrt(tau2_DL), + visuals={"ref_line": {"color": "C1", "label": f"DerSimonian–Laird τ = {np.sqrt(tau2_DL):.2f}"}}, +) +pc.get_viz("plot").legend(); +``` + +Three estimators, three commitments about how much the segments share. The fixed-effect ANOVA assumes one common effect and pools completely; the random-effects ANOVA admits between-segment variance and estimates it by moments; the hierarchical model carries that variance as a posterior. The grouping factor was the segment. Replace it with "study" and the model is untouched: meta-analysis is the random-effects analysis of variance with studies as the groups, and the index $k$ ranges over experiments rather than segments. The rest of this notebook makes exactly that substitution. Making that substitution is mechanical. What it reveals is substantive: once studies replace segments, τ becomes the quantity the replication programme was designed to estimate. + +## The hierarchical re-framing + +The model is the one we just fit, with markets in place of segments. Let $\theta_k$ be the true treatment effect in market $k$, and let $\hat d_k$ be the observed estimate from market $k$'s experiment with standard error $s_k$. The single-experiment view treats each $\hat d_k$ as the answer to its own question; vote-counting and pool-everything are degenerate cases of that view. The hierarchical view writes: + +$$ +\theta_k \sim \mathcal{N}(\mu, \tau), \qquad \hat d_k \mid \theta_k \sim \mathcal{N}(\theta_k, s_k), +$$ + +where $\mu$ is the population mean effect across markets and $\tau$ is the between-market standard deviation. $\mu$ tells the team what to expect on average; $\tau$ tells them how variable that expectation is across markets. Neither quantity is recoverable from any single experiment. Both are recoverable from the joint. + +```{code-cell} ipython3 +K = 8 +TRUE_MU = 0.4 +TRUE_TAU = 0.5 +SIGMA_OBS = 4.0 +MARKET_NAMES = [f"Market {chr(65 + i)}" for i in range(K)] +# Per-market sample sizes vary; smaller markets have noisier estimates, which +# is the regime where partial pooling does substantively visible work. +N_PER_MARKET = np.array([200, 250, 300, 350, 400, 500, 700, 1200]) +meta_rng = np.random.default_rng(20) + + +def simulate_meta_dataset_gaussian(K, N_per_market, true_mu, true_tau, sigma_obs, rng): + theta = rng.normal(true_mu, true_tau, size=K) + d_hat = np.zeros(K) + s = np.zeros(K) + for k in range(K): + N_k = int(N_per_market[k]) + y_A = rng.normal(10.0, sigma_obs, size=N_k) + y_B = rng.normal(10.0 + theta[k], sigma_obs, size=N_k) + d_hat[k] = y_B.mean() - y_A.mean() + s[k] = np.sqrt(y_A.var(ddof=1) / N_k + y_B.var(ddof=1) / N_k) + return theta, d_hat, s + + +true_theta, d_hat_obs, se_obs = simulate_meta_dataset_gaussian( + K, N_PER_MARKET, TRUE_MU, TRUE_TAU, SIGMA_OBS, meta_rng +) +markets_df = pd.DataFrame( + { + "market": MARKET_NAMES, + "N_per_arm": N_PER_MARKET, + "true_theta": true_theta, + "d_hat": d_hat_obs, + "se": se_obs, + "z_score": d_hat_obs / se_obs, + } +) +markets_df.round(3) +``` + +The per-market `z_score` column is what a frequentist replication exercise would consult: anything above 1.96 in absolute value counts as "significant", anything below does not. The columns disagree about how many markets "worked"; the underlying true effects disagree less. This is the gap the hierarchical model closes. The quantity no single experiment can recover is τ. + +## No pooling, complete pooling, partial pooling + +Three estimators reflect three commitments about how much the markets share. *No pooling* fits each market in isolation; the per-market estimate is $\hat d_k$. *Complete pooling* fits a single mean across all markets, treating them as draws from one distribution with no between-market variance. *Partial pooling* fits the hierarchical model above and lets the data weigh how exchangeable the markets are. The PyMC code below makes all three explicit so the shrinkage that distinguishes them becomes visible. + +```{code-cell} ipython3 +coords = {"market": MARKET_NAMES} + +with pm.Model(coords=coords) as complete_model: + mu_complete = pm.Normal("mu", mu=0.0, sigma=1.0) + pm.Normal("d_hat", mu=mu_complete, sigma=se_obs, observed=d_hat_obs, dims="market") + +with complete_model: + idata_complete = pm.sample( + draws=1000, + tune=1000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) + +with pm.Model(coords=coords) as partial_model: + mu = pm.Normal("mu", mu=0.0, sigma=1.0) + tau = pm.HalfNormal("tau", sigma=1.0) + theta_offset = pm.Normal("theta_offset", mu=0.0, sigma=1.0, dims="market") + theta = pm.Deterministic("theta", mu + tau * theta_offset, dims="market") + pm.Normal("d_hat", mu=theta, sigma=se_obs, observed=d_hat_obs, dims="market") + +with partial_model: + idata_partial = pm.sample( + draws=2000, + tune=2000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) +``` + +```{code-cell} ipython3 +no_pool_mean = d_hat_obs +no_pool_se = se_obs +complete_pool_mean = idata_complete.posterior["mu"].mean().item() +complete_pool_se = idata_complete.posterior["mu"].std().item() +partial_pool_summary = az.summary(idata_partial, var_names=["theta"], kind="stats") +partial_pool_mean = partial_pool_summary["mean"].values.astype(float) +partial_pool_sd = partial_pool_summary["sd"].values.astype(float) + +forest = pd.DataFrame( + { + "market": MARKET_NAMES, + "no_pool_mean": no_pool_mean, + "no_pool_lo": no_pool_mean - 1.96 * no_pool_se, + "no_pool_hi": no_pool_mean + 1.96 * no_pool_se, + "partial_mean": partial_pool_mean, + "partial_lo": partial_pool_mean - 1.96 * partial_pool_sd, + "partial_hi": partial_pool_mean + 1.96 * partial_pool_sd, + } +).round(3) + +fig, ax = plt.subplots(figsize=(20, 5.5)) +y_pos = np.arange(K) +ax.errorbar( + forest["no_pool_mean"], + y_pos - 0.18, + xerr=[ + forest["no_pool_mean"] - forest["no_pool_lo"], + forest["no_pool_hi"] - forest["no_pool_mean"], + ], + fmt="o", + color="C0", + label="No pooling", + capsize=3, +) +ax.errorbar( + forest["partial_mean"], + y_pos + 0.18, + xerr=[ + forest["partial_mean"] - forest["partial_lo"], + forest["partial_hi"] - forest["partial_mean"], + ], + fmt="s", + color="C3", + label="Partial pooling", + capsize=3, +) +ax.axvline( + complete_pool_mean, + color="black", + linestyle="--", + alpha=0.7, + label=f"Complete pooling (mean = {complete_pool_mean:.3f})", +) +ax.axvline(0.0, color="grey", linestyle=":", alpha=0.5) +ax.set_yticks(y_pos) +ax.set_yticklabels(MARKET_NAMES) +ax.set_xlabel("Estimated treatment effect") +ax.set_title("Forest plot: three pooling strategies on eight markets") +ax.legend(loc="upper right", bbox_to_anchor=(1.0, 1.0), framealpha=0.95) +plt.tight_layout(); +``` + +The partial-pooling estimates are pulled toward the population mean: the canonical *shrinkage* picture {cite:p}`gelman2006multilevel`, {cite:p}`gelman2020regression`. The pull is strongest for the markets whose individual estimates are noisiest (widest no-pooling intervals) or most extreme; it is weakest for markets whose estimates are tight and central. This is the data-driven version of "borrowing strength" that vote-counting cannot do and complete-pooling does only by force. + +```{code-cell} ipython3 +fig, ax = plt.subplots(figsize=(20, 5)) +for k in range(K): + ax.plot([0, 1], [no_pool_mean[k], partial_pool_mean[k]], color="grey", alpha=0.5, zorder=1) + ax.scatter(0, no_pool_mean[k], color="C0", zorder=3, s=55) + ax.scatter(1, partial_pool_mean[k], color="C3", zorder=3, s=55) + ax.text(1.04, partial_pool_mean[k], MARKET_NAMES[k], ha="left", va="center", fontsize=9) +ax.axhline( + complete_pool_mean, + color="black", + linestyle="--", + alpha=0.7, + label=f"Complete-pooling mean = {complete_pool_mean:.3f}", +) +ax.set_xticks([0, 1]) +ax.set_xticklabels(["No pooling", "Partial pooling"]) +ax.set_xlim(-0.15, 1.25) +ax.set_ylabel("Estimated treatment effect") +ax.set_title("Shrinkage: per-market estimates pulled toward the population mean") +ax.legend(loc="lower right"); +``` + +### The substance lives in $\tau$ + +The hierarchical model returns two population-level quantities, and the conventional reporting habit of leading with $\mu$ obscures the more important one. The posterior of $\tau$, the between-market standard deviation of true effects, is what tells the team how transportable any single result is to a new context. A small $\tau$ means the markets are nearly exchangeable, and the experiment generalises cleanly; a large $\tau$ means the markets are heterogeneous, and the next market is a meaningfully new experiment. Reporting only $\mu$ collapses this into a point and hides the variability that the next stakeholder will live with. + +```{code-cell} ipython3 +pc_mu = az.plot_dist( + idata_partial, + var_names=["mu"], + visuals={"title": {"text": r"Population mean $\mu$"}}, +) +az.add_lines( + pc_mu, + values=TRUE_MU, + visuals={"ref_line": {"color": "C2", "label": f"true = {TRUE_MU:.2f}"}}, +) +pc_mu.get_viz("plot").legend() + +pc_tau = az.plot_dist( + idata_partial, + var_names=["tau"], + visuals={"title": {"text": r"Between-market SD $\tau$"}}, +) +az.add_lines( + pc_tau, + values=TRUE_TAU, + visuals={"ref_line": {"color": "C2", "label": f"true = {TRUE_TAU:.2f}"}}, +) +pc_tau.get_viz("plot").legend(); +``` + +The posterior of $\tau$ is concentrated well away from zero, which is itself the result of substantive interest: the eight markets disagree about the size of the treatment effect in a way the data demand be respected. The conversion-rate version tells the same story, as we confirm next. + +## The same machinery on a binary outcome + +The conversion-rate version repeats the structure on the log-odds scale. Each market $k$ has its own baseline rate and its own treatment log-odds effect $\theta_k$; the population sits a level above ({cite:p}`carpenter2016hierarchical`). + +```{code-cell} ipython3 +TRUE_MU_LOGIT = 0.20 +TRUE_TAU_LOGIT = 0.25 +# Dedicated generator for the binary arm (as with `meta_rng`): keeps this section +# reproducible on its own and unaffected by the Gaussian arm's draws. +bern_rng = np.random.default_rng(2024) +BASELINE_RATES = bern_rng.beta(20, 180, size=K) + + +def simulate_meta_dataset_bernoulli( + K, N_per_market, baseline_rates, true_mu_logit, true_tau_logit, rng +): + from scipy.special import expit, logit + + theta = rng.normal(true_mu_logit, true_tau_logit, size=K) + n_A = np.zeros(K, dtype=int) + n_B = np.zeros(K, dtype=int) + for k in range(K): + p_A_k = baseline_rates[k] + p_B_k = expit(logit(p_A_k) + theta[k]) + n_A[k] = rng.binomial(int(N_per_market[k]), p_A_k) + n_B[k] = rng.binomial(int(N_per_market[k]), p_B_k) + return theta, n_A, n_B + + +true_theta_bern, n_A_obs, n_B_obs = simulate_meta_dataset_bernoulli( + K, N_PER_MARKET, BASELINE_RATES, TRUE_MU_LOGIT, TRUE_TAU_LOGIT, bern_rng +) +``` + +```{code-cell} ipython3 +with pm.Model(coords=coords) as partial_bern_model: + mu_logit = pm.Normal("mu", mu=0.0, sigma=0.5) + tau_logit = pm.HalfNormal("tau", sigma=0.5) + theta_offset = pm.Normal("theta_offset", mu=0.0, sigma=1.0, dims="market") + theta = pm.Deterministic("theta", mu_logit + tau_logit * theta_offset, dims="market") + baseline_logit = pm.Normal("baseline_logit", mu=-2.0, sigma=1.0, dims="market") + p_A = pm.Deterministic("p_A", pm.math.invlogit(baseline_logit), dims="market") + p_B = pm.Deterministic("p_B", pm.math.invlogit(baseline_logit + theta), dims="market") + pm.Binomial("obs_A", n=N_PER_MARKET, p=p_A, observed=n_A_obs, dims="market") + pm.Binomial("obs_B", n=N_PER_MARKET, p=p_B, observed=n_B_obs, dims="market") + +with partial_bern_model: + idata_partial_bern = pm.sample( + draws=2000, + tune=2000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) +``` + +```{code-cell} ipython3 +pc_mu = az.plot_dist( + idata_partial_bern, + var_names=["mu"], + visuals={"title": {"text": r"Population log-odds effect $\mu$"}}, +) +az.add_lines( + pc_mu, + values=TRUE_MU_LOGIT, + visuals={"ref_line": {"color": "C2", "label": f"true = {TRUE_MU_LOGIT:.2f}"}}, +) +pc_mu.get_viz("plot").legend() + +pc_tau = az.plot_dist( + idata_partial_bern, + var_names=["tau"], + visuals={"title": {"text": r"Between-market SD $\tau$ (log-odds)"}}, +) +az.add_lines( + pc_tau, + values=TRUE_TAU_LOGIT, + visuals={"ref_line": {"color": "C2", "label": f"true = {TRUE_TAU_LOGIT:.2f}"}}, +) +pc_tau.get_viz("plot").legend(); +``` + +The Bernoulli picture is the Gaussian picture on a different link. The population mean log-odds effect is recovered; the between-market variance is recovered; the per-market shrinkage works as before. The log-odds parameterisation carries a structural advantage the probability scale does not: a given value of τ means the same degree of between-market variability in the treatment effect regardless of what the baseline conversion rate happens to be. On the probability scale, a τ of 0.05 is meaningful heterogeneity at a 5\% baseline and negligible noise at a 50\% baseline; on the logit, τ is scale-invariant in the way the analysis needs it to be. + ++++ + +## How much to borrow + +With $\tau$ estimated on both scales, borrowing across markets raises a question the hierarchical model answers quietly: how far should one market's estimate move toward the others. The shrinkage already shown is that answer in action. Each market's pull toward the population mean is a weight set by its own precision against the between-market variance $\tau$ the data infer. + +```{code-cell} ipython3 +tau_post_mean = float(idata_partial.posterior["tau"].mean()) +shrinkage_weight = se_obs**2 / (se_obs**2 + tau_post_mean**2) +borrow_df = pd.DataFrame( + { + "market": MARKET_NAMES, + "se": se_obs, + "weight_on_population_mean": shrinkage_weight, + } +).round(3) +borrow_df +``` + +Noisy markets carry the largest weight on the population mean, so they borrow the most; precise markets keep their own estimate. The between-market variance sets the scale, and the data set $\tau$, so the borrowing rate adapts to the evidence. This is the dynamic borrowing the FDA guidance describes, where the amount borrowed responds to the similarity among the sources {cite:p}`fda2026bayesian`. + +Borrowing earns its keep through precision: a prior built from real past experiments sharpens the next posterior and lowers the sample size needed to reach a given assurance, so the eight markets already run are information the ninth should use. The open question is how much of it to grant, and a *power prior* makes that dial explicit {cite:p}`ibrahim2000power`. Raise the pooled likelihood from the past markets to a discount $\alpha$ in the unit interval and use the result as the prior for the new market. With $n_0$ past subjects it contributes about $\alpha\, n_0$ observations' worth of information, so $\alpha$ is the fraction of the historical sample size carried forward, the prior effective sample size {ref}`assurance_planning` planned around. At $\alpha = 1$ the past markets count in full, as if pooled; as $\alpha$ falls toward zero the prior widens and the borrowing fades. Fixing $\alpha$ in advance is what makes the power prior the static counterpart to the hierarchical model's data-driven $\tau$. + +The word *power* here means raising the likelihood to an exponent, a separate idea from the statistical power and assurance of {ref}`assurance_planning`. The two meet only through effective sample size: $\alpha$ sets how many past observations the prior is worth, and that count is the quantity the planning notebook traded against sample size. + +```{code-cell} ipython3 +w_pool = 1.0 / se_obs**2 +pooled_mean = float(np.sum(w_pool * d_hat_obs) / np.sum(w_pool)) +pooled_var = float(1.0 / np.sum(w_pool)) + +alpha_grid = np.array([0.1, 0.25, 0.5, 0.75, 1.0]) +power_prior_df = pd.DataFrame( + {"alpha": alpha_grid, "prior_mean": pooled_mean, "prior_sd": np.sqrt(pooled_var / alpha_grid)} +).round(3) +power_prior_df +``` + +The power prior must be measured against the belief the hierarchical model already holds about a market it has not seen. That belief is the model's *predictive distribution*, and it comes in two forms. The true-effect predictive gives the unknown effect of a new market drawn from the same population, + +$$\theta_{\text{new}} \mid \text{data} \sim \mathcal{N}\!\left(\mu_{\text{post}},\ \sqrt{\tau_{\text{post}}^2 + \sigma_{\mu,\text{post}}^2}\right),$$ + +and the observation predictive layers experimental noise on top, + +$$\hat d_{\text{new}} \mid \text{data} \sim \theta_{\text{new}} + \mathcal{N}(0, s_{\text{new}}).$$ + +We draw both now. The first sets the width the power prior is chasing; the second is the yardstick for the conflict check below. The power prior borrows the precision of the pooled mean and treats every market as one draw from a single shared effect, while the hierarchical predictive folds the between-market variation back in through $\tau$. The figure sets the two side by side. + +```{code-cell} ipython3 +mu_samples = idata_partial.posterior["mu"].values.flatten() +tau_samples = idata_partial.posterior["tau"].values.flatten() +rng_pp = np.random.default_rng(RANDOM_SEED + 1) +theta_new_samples = rng_pp.normal(mu_samples, tau_samples) +s_new = np.median(se_obs) +d_hat_new_samples = theta_new_samples + rng_pp.normal(0.0, s_new, size=len(theta_new_samples)) +``` + +```{code-cell} ipython3 +theta_new_mean = float(theta_new_samples.mean()) +theta_new_sd = float(theta_new_samples.std()) +alpha_match = ( + pooled_var / theta_new_sd**2 +) # discount at which the power prior reaches the tau-driven width +xx = np.linspace(pooled_mean - 1.2, pooled_mean + 1.2, 400) + +fig, ax = plt.subplots(figsize=(20, 4.5)) +for a in [1.0, 0.5, 0.1]: + sd_a = np.sqrt(pooled_var / a) + ax.plot(xx, stats.norm.pdf(xx, pooled_mean, sd_a), label=rf"Power prior, $\alpha$ = {a}") +ax.plot( + xx, + stats.norm.pdf(xx, pooled_mean, np.sqrt(pooled_var / alpha_match)), + color="C1", + linestyle="--", + label=rf"Power prior matching $\tau$ ($\alpha \approx$ {alpha_match:.2f})", +) +ax.plot( + xx, + stats.norm.pdf(xx, theta_new_mean, theta_new_sd), + color="black", + linewidth=2.5, + label=r"Hierarchical predictive ($\tau$-driven)", +) +ax.axvline(0.0, color="grey", linestyle=":", alpha=0.6) +ax.set_xlabel(r"Effect in a new market $\theta_{\text{new}}$") +ax.set_ylabel("Prior density") +ax.set_title("Static power prior versus dynamic hierarchical borrowing") +ax.legend(); +``` + +At $\alpha = 1$ the static power prior is the tightest curve, far more confident about a new market than the spread across markets warrants. Matching the hierarchical predictive takes a large deviation from full borrowing: the dashed curve marks the small $\alpha$ at which the static prior finally reaches the $\tau$-driven width, and that value has to be set by hand. The hierarchical model arrives there on its own, because $\tau$ reads the between-market spread from the data. + +Either prior becomes the belief the next market inherits, and that inheritance is legitimate only when the new market is drawn from the same population the past markets describe. Borrowing sharpens the posterior when that holds and pulls it toward the wrong centre when it fails, so the strength of borrowing has to be earned rather than assumed. A prior-data conflict check is the gate {cite:p}`evans2006checking`: locate the incoming estimate in the prior predictive distribution, and read a small tail probability as the new market disagreeing with the borrowed belief. + +```{code-cell} ipython3 +def prior_data_conflict_tail(d_new, prior_pred_samples): + centre = np.median(prior_pred_samples) + return float(np.mean(np.abs(prior_pred_samples - centre) >= abs(d_new - centre))) + + +concordant_d_new = 0.28 # a new market in line with the population +conflicting_d_new = -1.0 # a new market that contradicts the population +pd.DataFrame( + { + "incoming estimate": [concordant_d_new, conflicting_d_new], + "prior-predictive tail probability": [ + prior_data_conflict_tail(concordant_d_new, d_hat_new_samples), + prior_data_conflict_tail(conflicting_d_new, d_hat_new_samples), + ], + }, + index=["concordant market", "conflicting market"], +).round(3) +``` + +The concordant market sits in the body of the predictive and the tail probability is large; the prior and the new data describe one population, so the experiment can borrow at full strength and keep the precision that buys. The conflicting market sits far out and the tail probability is small, the trigger the guidance names for reassessing how much to borrow {cite:p}`fda2026bayesian`: lower $\alpha$, widen the prior, or hold the borrowed estimate aside until the discrepancy is understood. Dynamic borrowing through $\tau$ softens this failure on its own, since a heterogeneous set of markets produces a wide predictive that absorbs a surprising estimate, while a static power prior never adapts, so the analyst must run the check every time. Whatever borrowing strength passes the check is the prior the next experiment plans with. + ++++ + +## Predicting the next experiment + +The predictive we drew to calibrate borrowing also answers the question that occasioned the whole exercise: what will happen if we run the redesign in a market we have not tested yet. The two flavours now do decision work. The true-effect predictive $\theta_{\text{new}}$ is the best estimate of the effect in a new market; the observation predictive $\hat d_{\text{new}}$ is what to expect the next experiment to actually return, noise included. The gap between them is the experimental-noise envelope that a single-market estimate conflates with population variation. + +```{code-cell} ipython3 +dt = az.from_dict( + { + "posterior": { + "theta_new": theta_new_samples, + "d_hat_new": d_hat_new_samples, + } + }, + sample_dims=["sample"], +) + +pc = az.plot_dist( + dt, + kind="hist", + sample_dims=["sample"], + cols=[], + aes={"color": ["__variable__"]}, + visuals={ + "point_estimate": False, + "point_estimate_text": False, + "credible_interval": False, + "title": {"text": "Two predictive distributions for the ninth market"}, + }, +) +pc.add_legend("__variable__") +az.add_lines(pc, values=0.0, visuals={"ref_line": {"color": "black", "label": "0"}}); +``` + +```{code-cell} ipython3 +prob_theta_new_positive = float((theta_new_samples > 0).mean()) +prob_d_hat_new_positive = float((d_hat_new_samples > 0).mean()) +pd.DataFrame( + {"posterior probability > 0": [prob_theta_new_positive, prob_d_hat_new_positive]}, + index=[r"$\theta_{\text{new}}$ (true effect)", r"$\hat d_{\text{new}}$ (observed estimate)"], +).round(3) +``` + +The probability the true effect is positive in the next market is higher than the probability the next experiment will return a positive estimate. The gap is the experimental-noise tax: each individual experiment is a noisy realisation of an underlying truth, and the team will sometimes see a negative estimate even when the true effect is positive. Reporting the meta-analytic posterior on $\theta_{\text{new}}$ as the planning input for the next market, which {ref}`assurance_planning` then consumes as its prior, is the way to feed accumulating evidence forward without losing track of the noise. + ++++ + +## The synthesis becomes the next plan + +The predictive that calibrated borrowing also answers the question the planning notebook opens with. Read off its centre and width and the loop is closed explicitly: this synthesis is the prior {ref}`assurance_planning` integrates over. + +```{code-cell} ipython3 +# The true-effect predictive is exactly what the planning notebook treats as its +# prior: a Normal summarised by a location and a width. +planning_mu = round(float(theta_new_mean), 1) +planning_sigma = round(float(theta_new_sd), 1) +assurance_ceiling_next = 1.0 - stats.norm.cdf(0.0, planning_mu, planning_sigma) + +pd.DataFrame( + {"value": [planning_mu, planning_sigma, round(float(assurance_ceiling_next), 3)]}, + index=[ + "planning prior mean μ", + "planning prior sd σ", + "assurance ceiling P(θ_new > 0)", + ], +) +``` + +`EffectPrior(mu=planning_mu, sigma=planning_sigma)` is the object {ref}`assurance_planning` opens with. + ++++ + +## Replication as the data-generating process + +A single experiment is overheard speech. Eight experiments are conversation. The hierarchical model is what lets us hear them as conversation, and the posterior on the population describes the very population our experiments were drawn from. + +Replication is often described as a verification protocol, a post-hoc check on a result already in hand. It is better understood as the data-generating process whose distribution we are trying to learn. Each new market is a draw from a population we never observed directly; pooling constructs that population from the draws; the next experiment tests whether the constructed population keeps predicting new markets. The three notebooks make the same move on three problems. Planning became a posterior over the posteriors a future experiment will compute. Interpretation became a posterior over the bias a single experiment cannot rule out. Synthesis became a posterior over the population a series of experiments samples from. The likelihood changed from Gaussian to Bernoulli each time and the picture held. In each, an assumption a conventional analysis leaves implicit is made a parameter with a posterior, something to argue about rather than assume. The problem changes; its proper characterisation is always a posterior. + +And the last question feeds the first. The population this notebook inferred is the prior the planning notebook consumes: $\theta_{\text{new}} \sim \mathcal{N}(\mu, \tau)$ is the kind of belief {ref}`assurance_planning` integrates over before the next experiment is run. The synthesis that ends one experiment's lifecycle is the input to the design of the next. The lifecycle runs as a loop rather than a line from plan to verdict, and the posterior is what travels around it: each notebook's synthesis becomes the next notebook's prior, and each overheard conversation becomes the next one's opening question. + +## Authors + +- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026. + +## References + +:::{bibliography} +:filter: docname in docnames +::: + +## Watermark + +```{code-cell} ipython3 +%load_ext watermark +%watermark -n -u -v -iv -w -p pytensor,xarray +``` + +:::{include} ../page_footer.md +::: diff --git a/examples/causal_inference/sensitivity_unmeasured_confounding.ipynb b/examples/causal_inference/sensitivity_unmeasured_confounding.ipynb new file mode 100644 index 000000000..a5dd910c3 --- /dev/null +++ b/examples/causal_inference/sensitivity_unmeasured_confounding.ipynb @@ -0,0 +1,1078 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "dd69e77a", + "metadata": {}, + "source": [ + "(sensitivity_confounding)=\n", + "# Sensitivity Analysis for Unmeasured Confounding\n", + "\n", + ":::{post} May 2026\n", + ":tags: experimentation, sensitivity analysis, causal inference, confounding, robustness\n", + ":category: intermediate, reference\n", + ":author: Nathaniel Forde\n", + ":::\n", + "\n", + ":::{figure} experimentation_triptych.jpeg\n", + ":name: experimentation-triptych\n", + ":width: 100%\n", + ":align: center\n", + "\n", + "The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance:* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis (this notebook):* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis:* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery.\n", + ":::\n", + "\n", + "All applied inference is argument. Against every experiment you can set the contention that the working conditions were imperfect. Some aspect of the evaluation was flawed. Maybe treatment assignment introduced a subtle kind of bias, or the subjects didn't comply fully with the design. Against every experiment you can contrast the scientific ideal of perfect randomisation and clear adherence. Holding an experiment against that ideal is due diligence. Sensitivity analysis does it systematically, by varying how far the working conditions fall short of perfect randomisation.\n", + "\n", + "## The randomisation gap\n", + "\n", + "Randomisation is an assumption you maintain by design, not a fact you assert by intention. The checkout experiment ran, the headline effect on revenue-per-visitor looks positive, and somewhere in the diagnostic notes there is a line about compliance being 73%: users on slow connections were silently routed back to the old flow by a CDN edge case, and the routing was not random in the way it touched the population. The intent-to-treat estimate now depends on a counterfactual the experiment did not produce: what those users would have done under the new flow. Without further assumptions, the data cannot say what the treatment effect would have been if randomisation had held.\n", + "\n", + "This notebook develops the Bayesian response to this situation. Where Rosenbaum's $\\Gamma$ {cite:p}`rosenbaum2002observational` and the E-value {cite:p}`vanderweele2017sensitivity` give point summaries of how strong an unmeasured confounder would need to be to nullify the result, the Bayesian framing makes the same unmeasured confounder a *parameter* in the model, with a prior over its plausible strength and a posterior shaped by both the data and the analyst's commitments {cite:p}`imbens2003sensitivity`, {cite:p}`cinellihazlett2020omitted`. We develop the machinery on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the second of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The clean primary analysis of a well-run experiment, the posterior on the effect with the decision rule applied, appears as the demonstration step in {ref}`assurance_planning`; this notebook takes up the interpretation once that clean identification is itself in question.\n", + "\n", + ":::{admonition} Where this lands in regulatory practice\n", + ":class: note\n", + "\n", + "The sensitivity construction here follows the regulatory recommendation directly. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials describes sensitivity analysis as varying the prior over a critical assumption, and notes that \"some approaches can build uncertainty about specific assumptions into the prior itself\" {cite:p}`fda2026bayesian`, which is the move made below. The guidance goes further and sanctions modelling a discrepancy between data sources with \"an assumed bias parameter in the model\", the exact object this notebook places a prior on and sweeps. The clinical-trial setting differs from a product quasi-experiment; the bias parameter is the same.\n", + ":::" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "3abbded2", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:35:59.159236Z", + "iopub.status.busy": "2026-06-02T17:35:59.159124Z", + "iopub.status.idle": "2026-06-02T17:36:01.747061Z", + "shell.execute_reply": "2026-06-02T17:36:01.746567Z" + } + }, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pymc as pm\n", + "\n", + "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", + "warnings.filterwarnings(\"ignore\", category=UserWarning)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f669edc2", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:01.748523Z", + "iopub.status.busy": "2026-06-02T17:36:01.748381Z", + "iopub.status.idle": "2026-06-02T17:36:02.093165Z", + "shell.execute_reply": "2026-06-02T17:36:02.092571Z" + } + }, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = 'retina'\n", + "az.style.use(\"arviz-variat\")\n", + "rng = np.random.default_rng(7)\n", + "RANDOM_SEED = 7" + ] + }, + { + "cell_type": "markdown", + "id": "31dda6b3", + "metadata": {}, + "source": [ + "## What the data can and cannot say\n", + "\n", + "The structural picture is small and the notation traditional. Let $T$ be the observed treatment indicator (which flow the visitor actually saw), let $Y$ be the outcome (revenue), and let $U$ be an unmeasured user characteristic: connection quality, engagement disposition, whatever drives the differential compliance. Under randomisation $U$ is independent of $T$ by construction; under compliance failure $U$ is associated with $T$ and unobservable." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "dc1a9456", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:02.095069Z", + "iopub.status.busy": "2026-06-02T17:36:02.094831Z", + "iopub.status.idle": "2026-06-02T17:36:02.928579Z", + "shell.execute_reply": "2026-06-02T17:36:02.928074Z" + }, + "tags": [ + "hide-input" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 723, + "width": 3023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(15, 3.5))\n", + "ax.set_xlim(0, 10)\n", + "ax.set_ylim(0, 5)\n", + "ax.axis(\"off\")\n", + "\n", + "nodes = {\"T\": (2, 1.5), \"Y\": (8, 1.5), \"U\": (5, 4)}\n", + "for name, (x, y) in nodes.items():\n", + " ax.scatter(x, y, s=2200, facecolor=\"white\", edgecolor=\"black\", zorder=3)\n", + " ax.text(x, y, name, ha=\"center\", va=\"center\", fontsize=16, zorder=4)\n", + "\n", + "\n", + "def arrow(a, b, **kw):\n", + " (x0, y0), (x1, y1) = nodes[a], nodes[b]\n", + " ax.annotate(\n", + " \"\",\n", + " xy=(x1, y1),\n", + " xytext=(x0, y0),\n", + " arrowprops=dict(arrowstyle=\"->\", lw=2, shrinkA=22, shrinkB=22, **kw),\n", + " )\n", + "\n", + "\n", + "arrow(\"T\", \"Y\")\n", + "arrow(\"U\", \"T\", color=\"firebrick\")\n", + "arrow(\"U\", \"Y\", color=\"firebrick\")\n", + "\n", + "ax.text(5, 1.8, r\"$\\tau$ (causal effect)\", ha=\"center\", fontsize=11)\n", + "ax.text(3.2, 3.3, r\"$\\lambda_T$\", color=\"firebrick\", fontsize=12)\n", + "ax.text(6.8, 3.3, r\"$\\lambda_Y$\", color=\"firebrick\", fontsize=12)\n", + "ax.set_title(\"The identification gap: $U$ unobserved\", fontsize=12);" + ] + }, + { + "cell_type": "markdown", + "id": "e8f31fe6", + "metadata": {}, + "source": [ + "What we want is $\\tau$, the causal effect of $T$ on $Y$. What the data identify is $\\tau$ *plus* the contribution of any path that flows through $U$: the product of the two red edges, collected into a single bias term $\\beta = \\lambda_T \\cdot \\lambda_Y / \\mathrm{var}(T)$ at the scale of the observed difference in means {cite:p}`hernan2020whatif`, {cite:p}`cunningham2021causal`. The naïve estimator returns $\\tau + \\beta$. The data are silent on the decomposition; the prior is what sets it.\n", + "\n", + "## The bias parameter\n", + "\n", + "The Bayesian sensitivity analysis makes $\\beta$ a model parameter with a prior. The data inform the sum $\\tau + \\beta$ through the observed difference; the prior on $\\beta$ controls how much of that sum is attributed to the unmeasured confounder rather than to the treatment. Three prior commitments:\n", + "\n", + "- **Dismissive prior** ($\\beta \\sim \\mathcal{N}(0, 0.05)$): \"I am confident there is essentially no confounding.\"\n", + "- **Moderate prior** ($\\beta \\sim \\mathcal{N}(0, 0.3)$): \"I will allow that confounding may have shifted the apparent effect by up to a few tenths of a revenue unit.\"\n", + "- **Sceptical prior** ($\\beta \\sim \\mathcal{N}(0, 0.7)$): \"I will not commit to confounding being small; the data must speak loudly to be heard.\"\n", + "\n", + "Each is an auditable commitment." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9d37c3cd", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:02.930162Z", + "iopub.status.busy": "2026-06-02T17:36:02.929961Z", + "iopub.status.idle": "2026-06-02T17:36:02.933311Z", + "shell.execute_reply": "2026-06-02T17:36:02.932936Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Observed difference d_hat = 0.793 (sampling SE = 0.089)\n", + "True tau = 0.3, true bias = 0.5, true sum = 0.8\n" + ] + } + ], + "source": [ + "N = 4000\n", + "TRUE_TAU = 0.30\n", + "TRUE_BIAS = 0.50\n", + "SIGMA_OBS = 4.0\n", + "\n", + "\n", + "def simulate_quasi_experimental_gaussian(N, true_tau, true_bias, sigma_obs, rng):\n", + " baseline = 10.0\n", + " y_A = rng.normal(baseline, sigma_obs, size=N)\n", + " y_B = rng.normal(baseline + true_tau + true_bias, sigma_obs, size=N)\n", + " return y_A, y_B\n", + "\n", + "\n", + "y_A_obs, y_B_obs = simulate_quasi_experimental_gaussian(N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, rng)\n", + "d_hat = y_B_obs.mean() - y_A_obs.mean()\n", + "sigma_d = np.sqrt(2 * SIGMA_OBS**2 / N)\n", + "print(f\"Observed difference d_hat = {d_hat:.3f} (sampling SE = {sigma_d:.3f})\")\n", + "print(f\"True tau = {TRUE_TAU}, true bias = {TRUE_BIAS}, true sum = {TRUE_TAU + TRUE_BIAS}\")" + ] + }, + { + "cell_type": "markdown", + "id": "ba7bfe6c", + "metadata": {}, + "source": [ + "The observed difference recovers the *biased* effect, as it must. $\\tau$ is what we want; $\\beta$ is what we cannot observe. Before asking how a prior reshapes that sum, confirm the machinery is faithful: hand the model the belief an analyst would hold if they knew the confounder exactly, a prior on $\\beta$ centred at the true bias, and the treatment effect should return unbiased across repeated experiments." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "39981d0f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:02.935072Z", + "iopub.status.busy": "2026-06-02T17:36:02.934958Z", + "iopub.status.idle": "2026-06-02T17:36:03.173574Z", + "shell.execute_reply": "2026-06-02T17:36:03.173186Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 823, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_sensitivity_posterior(\n", + " d_hat, sigma_d, tau_prior_sd, bias_prior_sd, tau_prior_mean=0.0, bias_prior_mean=0.0\n", + "):\n", + " \"\"\"Closed-form posterior over (tau, beta) given the observed effect.\"\"\"\n", + " prior_precision = np.diag([1.0 / tau_prior_sd**2, 1.0 / bias_prior_sd**2])\n", + " F = np.array([[1.0, 1.0]])\n", + " data_precision = F.T @ F / sigma_d**2\n", + " post_precision = prior_precision + data_precision\n", + " post_cov = np.linalg.inv(post_precision)\n", + " prior_mean = np.array([tau_prior_mean, bias_prior_mean])\n", + " rhs = prior_precision @ prior_mean + F.flatten() * d_hat / sigma_d**2\n", + " post_mean = post_cov @ rhs\n", + " return post_mean, post_cov\n", + "\n", + "\n", + "# Across many synthetic quasi-experiments, where does the posterior mean of tau land\n", + "# when the analyst's prior on the bias is centred at the true confounding strength?\n", + "recovery_rng = np.random.default_rng(RANDOM_SEED)\n", + "n_recovery = 500\n", + "tau_posterior_means = np.empty(n_recovery)\n", + "for i in range(n_recovery):\n", + " y_A_i, y_B_i = simulate_quasi_experimental_gaussian(\n", + " N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, recovery_rng\n", + " )\n", + " d_hat_i = y_B_i.mean() - y_A_i.mean()\n", + " post_mean_i, _ = gaussian_sensitivity_posterior(\n", + " d_hat_i, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.1, bias_prior_mean=TRUE_BIAS\n", + " )\n", + " tau_posterior_means[i] = post_mean_i[0]\n", + "\n", + "fig, ax = plt.subplots(figsize=(20, 4))\n", + "ax.hist(tau_posterior_means, bins=30, color=\"C0\", alpha=0.7, edgecolor=\"white\")\n", + "ax.axvline(TRUE_TAU, color=\"C2\", linestyle=\"--\", linewidth=2, label=f\"true \\u03c4 = {TRUE_TAU:.2f}\")\n", + "ax.axvline(\n", + " tau_posterior_means.mean(),\n", + " color=\"C3\",\n", + " linewidth=2,\n", + " label=f\"mean estimate = {tau_posterior_means.mean():.3f}\",\n", + ")\n", + "ax.set_xlabel(r\"Posterior mean of $\\tau$ across simulated experiments\")\n", + "ax.set_ylabel(\"Frequency\")\n", + "ax.set_title(r\"Recovery of $\\tau$ when the bias prior is correctly centred\")\n", + "ax.legend();" + ] + }, + { + "cell_type": "markdown", + "id": "054df778", + "metadata": {}, + "source": [ + "The sampling distribution of the posterior mean sits on the true $\\tau = 0.30$: with the confounder's strength correctly specified, the estimator is unbiased across repeated experiments. The recovery is real, but read what produced it. The data fixed the sum $\\tau + \\beta$ through the observed difference; the correctly-centred prior on $\\beta$ is what split that sum into its parts. A single difference in means cannot separate a treatment effect from a confound that imitates it. The data identify the two only in combination with a commitment about the confounder. The prior is the content of that decomposition, which is why an honest analysis varies it rather than fixing it. Recentre the prior on $\\beta$ at zero, where an analyst lands by default with no oracle for the confounder's size, and the estimate moves. The moderate prior below makes the shift concrete." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "7d543aca", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:03.174922Z", + "iopub.status.busy": "2026-06-02T17:36:03.174827Z", + "iopub.status.idle": "2026-06-02T17:36:05.724139Z", + "shell.execute_reply": "2026-06-02T17:36:05.723669Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "NUTS[nutpie]: [tau, beta]\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 559, + "width": 2423 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_sensitivity_model(d_hat, sigma_d, tau_prior=(0.0, 1.0), bias_prior=(0.0, 0.3)):\n", + " with pm.Model() as model:\n", + " tau = pm.Normal(\"tau\", mu=tau_prior[0], sigma=tau_prior[1])\n", + " beta = pm.Normal(\"beta\", mu=bias_prior[0], sigma=bias_prior[1])\n", + " observed_effect = pm.Deterministic(\"observed_effect\", tau + beta)\n", + " pm.Normal(\"d_hat\", mu=observed_effect, sigma=sigma_d, observed=d_hat)\n", + " return model\n", + "\n", + "\n", + "with gaussian_sensitivity_model(d_hat, sigma_d, bias_prior=(0.0, 0.3)):\n", + " idata_moderate = pm.sample(\n", + " draws=2000,\n", + " tune=2000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )\n", + "\n", + "az.plot_dist(idata_moderate, var_names=[\"tau\", \"beta\"])\n", + "axes = plt.gcf().axes\n", + "for a in axes:\n", + " a.set_title(\"\")\n", + "axes[0].axvline(TRUE_TAU, color=\"C2\", linestyle=\"--\", label=f\"true τ = {TRUE_TAU:.2f}\")\n", + "axes[0].legend()\n", + "axes[1].axvline(TRUE_BIAS, color=\"C2\", linestyle=\"--\", label=f\"true β = {TRUE_BIAS:.2f}\")\n", + "axes[1].legend()\n", + "plt.suptitle(r\"Posterior of $\\tau$ and $\\beta$ under a moderate bias prior\");" + ] + }, + { + "cell_type": "markdown", + "id": "74929da4", + "metadata": {}, + "source": [ + "Under the moderate prior, centred at zero, the posterior of $\\tau$ is pulled well above the true 0.30 and the posterior of $\\beta$ settles near zero: with no prior reason to expect a confounder, the treatment absorbs the sum. The true $\\beta = 0.50$ falls in the prior's right tail. The data informed the sum; the prior shaped the split.\n", + "\n", + "### Tipping-point analysis under a Gaussian outcome\n", + "\n", + "The model with a flat prior on $\\tau$ and a Gaussian prior on $\\beta$ is fully conjugate; the posterior is a closed-form bivariate Normal that we can compute analytically. This lets us trace the tipping point: the bias prior strength at which the posterior probability of a positive treatment effect drops below the team's decision threshold." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2f6ee70f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:05.725817Z", + "iopub.status.busy": "2026-06-02T17:36:05.725672Z", + "iopub.status.idle": "2026-06-02T17:36:05.746568Z", + "shell.execute_reply": "2026-06-02T17:36:05.746120Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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beta0.0650.290.0650.287
\n", + "
" + ], + "text/plain": [ + " MCMC Analytical \n", + " mean sd mean sd\n", + "tau 0.72 0.3 0.722 0.299\n", + "beta 0.065 0.29 0.065 0.287" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Verify the closed form agrees with MCMC under the moderate prior\n", + "post_mean_anly, post_cov_anly = gaussian_sensitivity_posterior(\n", + " d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.3\n", + ")\n", + "mcmc_summary = az.summary(idata_moderate, var_names=[\"tau\", \"beta\"], kind=\"stats\")[[\"mean\", \"sd\"]]\n", + "analytical_summary = pd.DataFrame(\n", + " {\"mean\": post_mean_anly, \"sd\": np.sqrt(np.diag(post_cov_anly))},\n", + " index=[\"tau\", \"beta\"],\n", + ")\n", + "pd.concat({\"MCMC\": mcmc_summary, \"Analytical\": analytical_summary}, axis=1).round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "3d2acc0d", + "metadata": {}, + "source": [ + "The two posteriors agree. The analytical form carries the sweep." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e9d91b3f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:05.747862Z", + "iopub.status.busy": "2026-06-02T17:36:05.747780Z", + "iopub.status.idle": "2026-06-02T17:36:06.105478Z", + "shell.execute_reply": "2026-06-02T17:36:06.104918Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 823, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import stats\n", + "\n", + "bias_sd_grid = np.linspace(0.001, 1.0, 40)\n", + "sweep_records = []\n", + "for bias_sd in bias_sd_grid:\n", + " pm_a, pc_a = gaussian_sensitivity_posterior(\n", + " d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=bias_sd\n", + " )\n", + " tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0])\n", + " prob_positive = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd)\n", + " sweep_records.append(\n", + " {\"bias_sd\": bias_sd, \"tau_mean\": tau_mean, \"tau_sd\": tau_sd, \"prob_positive\": prob_positive}\n", + " )\n", + "sweep_df = pd.DataFrame(sweep_records)\n", + "\n", + "decision_threshold = 0.95\n", + "above_threshold = sweep_df[sweep_df[\"prob_positive\"] >= decision_threshold]\n", + "tipping_point = above_threshold[\"bias_sd\"].max() if len(above_threshold) else np.nan\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(20, 4))\n", + "axes[0].plot(\n", + " sweep_df[\"bias_sd\"],\n", + " sweep_df[\"tau_mean\"],\n", + " linewidth=2,\n", + " color=\"C0\",\n", + " label=r\"Posterior mean of $\\tau$\",\n", + ")\n", + "axes[0].fill_between(\n", + " sweep_df[\"bias_sd\"],\n", + " sweep_df[\"tau_mean\"] - sweep_df[\"tau_sd\"],\n", + " sweep_df[\"tau_mean\"] + sweep_df[\"tau_sd\"],\n", + " alpha=0.25,\n", + " color=\"C0\",\n", + " label=r\"$\\pm 1$ SD\",\n", + ")\n", + "axes[0].axhline(0.0, color=\"black\", linestyle=\":\")\n", + "axes[0].set_xlabel(r\"Prior SD on bias $\\beta$\")\n", + "axes[0].set_ylabel(r\"Posterior of $\\tau$\")\n", + "axes[0].set_title(\"Posterior shifts as the bias prior loosens\")\n", + "axes[0].legend()\n", + "\n", + "axes[1].plot(sweep_df[\"bias_sd\"], sweep_df[\"prob_positive\"], linewidth=2, color=\"C3\")\n", + "axes[1].axhline(\n", + " decision_threshold,\n", + " color=\"black\",\n", + " linestyle=\"--\",\n", + " label=f\"Decision threshold = {decision_threshold}\",\n", + ")\n", + "if not np.isnan(tipping_point):\n", + " axes[1].axvline(\n", + " tipping_point,\n", + " color=\"C3\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=f\"Tipping point ≈ {tipping_point:.2f}\",\n", + " )\n", + "axes[1].set_xlabel(r\"Prior SD on bias $\\beta$\")\n", + "axes[1].set_ylabel(r\"$P(\\tau > 0 \\mid d_{\\text{obs}})$\")\n", + "axes[1].set_title(\"Tipping point in the decision rule\")\n", + "axes[1].legend();" + ] + }, + { + "cell_type": "markdown", + "id": "e15e75ee", + "metadata": {}, + "source": [ + "Read the left panel from left to right: as the analyst loosens their prior on the bias, the posterior mean of $\\tau$ drifts downward and the posterior interval widens. Read the right panel: there is a bias prior strength at which the posterior probability of a positive effect falls below the conventional decision threshold. The tipping point is a price tag on the claim rather than a refutation of the experiment. To assert a positive effect requires a stated belief that the bias prior is *tighter* than the tipping point. The honest version of the conversation with stakeholders runs through this number. The posterior is what makes that conversation possible: the same inference machinery that reads the experiment's results in a clean world is what traces the contour of its fragility here. The question has shifted from what the treatment did to which commitments about the unmeasured bias are needed to believe it did anything, and a posterior answers the new question as readily as the old.\n", + "\n", + "The same machinery runs on the log-odds scale. Before mapping the full topology of the bias-prior space, we confirm that the one-dimensional fragility picture is not an artefact of the Gaussian likelihood." + ] + }, + { + "cell_type": "markdown", + "id": "22d603ff", + "metadata": {}, + "source": [ + "## The same machinery on a binary outcome\n", + "\n", + "The conversion-rate version of the experiment uses the same structural model on the log-odds scale. The bias parameter now lives on the logit, but the framing is identical: the observed log-odds difference is the sum of a treatment effect and an unmeasured-confounder contribution, and a prior over the latter is the only thing that separates them." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "97c262c4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:06.107055Z", + "iopub.status.busy": "2026-06-02T17:36:06.106914Z", + "iopub.status.idle": "2026-06-02T17:36:06.110905Z", + "shell.execute_reply": "2026-06-02T17:36:06.110266Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Observed conversions: A = 834/8000, B = 1165/8000\n", + "True p_A = 0.1000, p_B (with bias) = 0.1484\n" + ] + } + ], + "source": [ + "def simulate_quasi_experimental_bernoulli(N, baseline_rate, true_tau_logit, true_bias_logit, rng):\n", + " from scipy.special import expit\n", + "\n", + " p_A = expit(np.log(baseline_rate / (1 - baseline_rate)))\n", + " p_B = expit(np.log(baseline_rate / (1 - baseline_rate)) + true_tau_logit + true_bias_logit)\n", + " n_A = rng.binomial(N, p_A)\n", + " n_B = rng.binomial(N, p_B)\n", + " return n_A, n_B, p_A, p_B\n", + "\n", + "\n", + "BASELINE_RATE_B = 0.10\n", + "TRUE_TAU_LOGIT = 0.15\n", + "TRUE_BIAS_LOGIT = 0.30\n", + "\n", + "n_A_obs, n_B_obs, p_A_true, p_B_true = simulate_quasi_experimental_bernoulli(\n", + " N=8000,\n", + " baseline_rate=BASELINE_RATE_B,\n", + " true_tau_logit=TRUE_TAU_LOGIT,\n", + " true_bias_logit=TRUE_BIAS_LOGIT,\n", + " rng=rng,\n", + ")\n", + "print(f\"Observed conversions: A = {n_A_obs}/8000, B = {n_B_obs}/8000\")\n", + "print(f\"True p_A = {p_A_true:.4f}, p_B (with bias) = {p_B_true:.4f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "e0f3171d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:06.112390Z", + "iopub.status.busy": "2026-06-02T17:36:06.112290Z", + "iopub.status.idle": "2026-06-02T17:36:10.955670Z", + "shell.execute_reply": "2026-06-02T17:36:10.954860Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "NUTS[nutpie]: [logit_p_A, tau, beta]\n", + "NUTS[nutpie]: [logit_p_A, tau, beta]\n", + "NUTS[nutpie]: [logit_p_A, tau, beta]\n", + "NUTS[nutpie]: [logit_p_A, tau, beta]\n", + "NUTS[nutpie]: [logit_p_A, tau, beta]\n", + "NUTS[nutpie]: [logit_p_A, tau, beta]\n" + ] + }, + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " bias_sd tau_mean tau_sd prob_positive\n", + "0 0.05 0.369 0.070 1.000\n", + "1 0.15 0.358 0.146 0.998\n", + "2 0.20 0.324 0.193 0.955\n", + "3 0.30 0.273 0.267 0.835\n", + "4 0.50 0.191 0.342 0.716\n", + "5 0.80 0.110 0.401 0.600" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def bernoulli_sensitivity_model(\n", + " n_A, n_B, N, baseline_logit_prior=(-2.0, 0.5), tau_prior=(0.0, 0.5), bias_prior=(0.0, 0.3)\n", + "):\n", + " with pm.Model() as model:\n", + " logit_p_A = pm.Normal(\n", + " \"logit_p_A\", mu=baseline_logit_prior[0], sigma=baseline_logit_prior[1]\n", + " )\n", + " tau = pm.Normal(\"tau\", mu=tau_prior[0], sigma=tau_prior[1])\n", + " beta = pm.Normal(\"beta\", mu=bias_prior[0], sigma=bias_prior[1])\n", + " logit_p_B = pm.Deterministic(\"logit_p_B\", logit_p_A + tau + beta)\n", + " p_A = pm.Deterministic(\"p_A\", pm.math.invlogit(logit_p_A))\n", + " p_B = pm.Deterministic(\"p_B\", pm.math.invlogit(logit_p_B))\n", + " pm.Binomial(\"obs_A\", n=N, p=p_A, observed=n_A)\n", + " pm.Binomial(\"obs_B\", n=N, p=p_B, observed=n_B)\n", + " return model\n", + "\n", + "\n", + "tipping_records_bern = []\n", + "for bias_sd in [0.05, 0.15, 0.2, 0.30, 0.50, 0.80]:\n", + " with bernoulli_sensitivity_model(n_A_obs, n_B_obs, N=8000, bias_prior=(0.0, bias_sd)):\n", + " idata = pm.sample(\n", + " draws=1000,\n", + " tune=1000,\n", + " chains=2,\n", + " target_accept=0.95,\n", + " random_seed=RANDOM_SEED,\n", + " progressbar=False,\n", + " )\n", + " tau_samples = idata.posterior[\"tau\"].values.flatten()\n", + " tipping_records_bern.append(\n", + " {\n", + " \"bias_sd\": bias_sd,\n", + " \"tau_mean\": tau_samples.mean(),\n", + " \"tau_sd\": tau_samples.std(),\n", + " \"prob_positive\": float((tau_samples > 0).mean()),\n", + " }\n", + " )\n", + "tipping_bern_df = pd.DataFrame(tipping_records_bern)\n", + "# prob_positive decreases as the bias prior loosens; interpolate to the threshold crossing\n", + "tip_bern = float(\n", + " np.interp(\n", + " decision_threshold,\n", + " tipping_bern_df[\"prob_positive\"].values[::-1],\n", + " tipping_bern_df[\"bias_sd\"].values[::-1],\n", + " )\n", + ")\n", + "tipping_bern_df.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "69190ddc", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:10.957347Z", + "iopub.status.busy": "2026-06-02T17:36:10.957218Z", + "iopub.status.idle": "2026-06-02T17:36:11.260109Z", + "shell.execute_reply": "2026-06-02T17:36:11.259622Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 823, + "width": 4023 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(20, 4))\n", + "axes[0].errorbar(\n", + " tipping_bern_df[\"bias_sd\"],\n", + " tipping_bern_df[\"tau_mean\"],\n", + " yerr=tipping_bern_df[\"tau_sd\"],\n", + " marker=\"o\",\n", + " linewidth=2,\n", + " capsize=4,\n", + ")\n", + "axes[0].axhline(0.0, color=\"black\", linestyle=\":\")\n", + "axes[0].set_xlabel(r\"Prior SD on bias $\\beta$ (log-odds)\")\n", + "axes[0].set_ylabel(r\"Posterior of $\\tau$ (log-odds)\")\n", + "axes[0].set_title(\"Bernoulli case: posterior of treatment effect\")\n", + "\n", + "axes[1].plot(\n", + " tipping_bern_df[\"bias_sd\"],\n", + " tipping_bern_df[\"prob_positive\"],\n", + " marker=\"o\",\n", + " linewidth=2,\n", + " color=\"C3\",\n", + ")\n", + "axes[1].axhline(\n", + " decision_threshold,\n", + " color=\"black\",\n", + " linestyle=\"--\",\n", + " label=f\"Decision threshold = {decision_threshold}\",\n", + ")\n", + "axes[1].axvline(\n", + " tip_bern,\n", + " color=\"C3\",\n", + " linestyle=\":\",\n", + " alpha=0.7,\n", + " label=f\"Tipping point ≈ {tip_bern:.2f}\",\n", + ")\n", + "axes[1].set_xlabel(r\"Prior SD on bias $\\beta$ (log-odds)\")\n", + "axes[1].set_ylabel(r\"$P(\\tau > 0 \\mid \\text{data})$\")\n", + "axes[1].set_title(\"Tipping point on the log-odds scale\")\n", + "axes[1].legend();" + ] + }, + { + "cell_type": "markdown", + "id": "a03b1409", + "metadata": {}, + "source": [ + "The shape of the curve confirms what the Gaussian case showed: the decision rule loses confidence as the prior on bias widens, and the tipping point is identifiable on the log-odds scale just as it was on the revenue scale. The E-value of {cite:p}`vanderweele2017sensitivity` corresponds, roughly, to the bias magnitude at which a frequentist decision would tip; the Bayesian curve is the full posterior over that commitment. One dimension, two likelihoods, the same fragility picture. The complete audit needs both dimensions of the bias prior, the full region of commitments the conclusion can survive. That surface is below." + ] + }, + { + "cell_type": "markdown", + "id": "ad6b05cf", + "metadata": {}, + "source": [ + "### The sensitivity surface\n", + "\n", + "Both the Gaussian and the binary sweep moved one dimension of the bias prior. The complete audit requires the other: a map of the full region of $(\\mu_\\beta, \\sigma_\\beta)$ commitments the experiment can survive. The sweep below opens the line into a surface." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "c46490fc", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:11.261451Z", + "iopub.status.busy": "2026-06-02T17:36:11.261355Z", + "iopub.status.idle": "2026-06-02T17:36:12.083932Z", + "shell.execute_reply": "2026-06-02T17:36:12.083206Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 1023, + "width": 3016 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "bias_mu_grid = np.linspace(-0.5, 0.5, 25)\n", + "bias_sd_grid_2d = np.linspace(0.01, 1.0, 25)\n", + "prob_grid = np.zeros((len(bias_sd_grid_2d), len(bias_mu_grid)))\n", + "\n", + "for i, b_sd in enumerate(bias_sd_grid_2d):\n", + " for j, b_mu in enumerate(bias_mu_grid):\n", + " pm_a, pc_a = gaussian_sensitivity_posterior(\n", + " d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=b_sd, bias_prior_mean=b_mu\n", + " )\n", + " tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0])\n", + " prob_grid[i, j] = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd)\n", + "\n", + "fig, ax = plt.subplots(figsize=(15, 5))\n", + "im = ax.imshow(\n", + " prob_grid,\n", + " origin=\"lower\",\n", + " aspect=\"auto\",\n", + " extent=[bias_mu_grid.min(), bias_mu_grid.max(), bias_sd_grid_2d.min(), bias_sd_grid_2d.max()],\n", + " cmap=\"RdBu_r\",\n", + " vmin=0.0,\n", + " vmax=1.0,\n", + ")\n", + "contour = ax.contour(\n", + " bias_mu_grid,\n", + " bias_sd_grid_2d,\n", + " prob_grid,\n", + " levels=[0.5, decision_threshold],\n", + " colors=[\"white\", \"black\"],\n", + " linewidths=[1.2, 2.0],\n", + ")\n", + "ax.clabel(contour, fmt={0.5: \"P=0.5\", decision_threshold: f\"P={decision_threshold}\"})\n", + "ax.set_xlabel(r\"Prior mean of bias $\\beta$\")\n", + "ax.set_ylabel(r\"Prior SD of bias $\\beta$\")\n", + "ax.set_title(r\"$P(\\tau > 0)$ under bias-prior commitments\")\n", + "plt.colorbar(im, ax=ax, label=r\"$P(\\tau > 0 \\mid d_{\\text{obs}})$\");" + ] + }, + { + "cell_type": "markdown", + "id": "13d4a25c", + "metadata": {}, + "source": [ + "The decision threshold contour partitions the bias-prior plane into a region where the experiment is defensible and a region where it is not. The analyst who wants to claim a positive effect commits to a point inside the inner contour. The dissenter who wants to claim the effect is artefactual commits to a point outside it. The graph locates the disagreement rather than settling it. It shows which region of the bias-prior plane each party's commitments occupy, and whether that region sits inside or outside the contour of defensibility. The audit has a legible geometry." + ] + }, + { + "cell_type": "markdown", + "id": "6bea675c", + "metadata": {}, + "source": [ + "## Robustness as a posterior question\n", + "\n", + "A sensitivity analysis maps the randomisation gap rather than closing it. The sweep above does not prove the experiment robust; it produces an auditable exhibit of which bias commitments the experiment can survive and which it cannot. That exhibit is the deliverable.\n", + "\n", + "This changes what honest reporting looks like. The headline from a quasi-experiment becomes the *tipping point*, the prior on the bias at which the conclusion turns, and the sensitivity surface widens that point into a region: the full set of bias-prior commitments the experiment can survive, with its boundary drawn as a contour. Two analysts who hold the same data and reach opposite conclusions are reading the same difference in means through different priors on the confounder, and the surface shows precisely which commitment divides them.\n", + "\n", + "What a clean experiment reports as one posterior on the effect, a quasi-experiment reports as a posterior spread over the bias the data cannot rule out. Mapping that spread, and naming the commitment a positive conclusion requires, is what the quasi-experiment owes its readers. {ref}`meta_analysis_experiments` turns from a single threatened experiment to a whole series of them.\n", + "\n", + "## Authors\n", + "\n", + "- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026.\n", + "\n", + "## References\n", + "\n", + ":::{bibliography}\n", + ":filter: docname in docnames\n", + ":::\n", + "\n", + "## Watermark" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "66eea177", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-02T17:36:12.085879Z", + "iopub.status.busy": "2026-06-02T17:36:12.085748Z", + "iopub.status.idle": "2026-06-02T17:36:12.100168Z", + "shell.execute_reply": "2026-06-02T17:36:12.099634Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last updated: Fri, 12 Jun 2026\n", + "\n", + "Python implementation: CPython\n", + "Python version : 3.13.13\n", + "IPython version : 9.14.0\n", + "\n", + "pytensor: 3.0.3\n", + "xarray : 2026.4.0\n", + "\n", + "arviz : 1.1.0\n", + "matplotlib: 3.10.9\n", + "numpy : 2.3.5\n", + "pandas : 2.3.3\n", + "pymc : 6.0.1\n", + "scipy : 1.17.1\n", + "\n", + "Watermark: 2.6.0\n", + "\n" + ] + } + ], + "source": [ + "%load_ext watermark\n", + "%watermark -n -u -v -iv -w -p pytensor,xarray" + ] + }, + { + "cell_type": "markdown", + "id": "edf11e5a", + "metadata": {}, + "source": [ + ":::{include} ../page_footer.md\n", + ":::" + ] + } + ], + "metadata": { + "jupytext": { + "default_lexer": "ipython3" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/causal_inference/sensitivity_unmeasured_confounding.myst.md b/examples/causal_inference/sensitivity_unmeasured_confounding.myst.md new file mode 100644 index 000000000..8a4b5941b --- /dev/null +++ b/examples/causal_inference/sensitivity_unmeasured_confounding.myst.md @@ -0,0 +1,504 @@ +--- +jupytext: + default_lexer: ipython3 + text_representation: + extension: .md + format_name: myst + format_version: 0.13 +kernelspec: + display_name: Python 3 + language: python + name: python3 +--- + +(sensitivity_confounding)= +# Sensitivity Analysis for Unmeasured Confounding + +:::{post} May 2026 +:tags: experimentation, sensitivity analysis, causal inference, confounding, robustness +:category: intermediate, reference +:author: Nathaniel Forde +::: + +:::{figure} experimentation_triptych.jpeg +:name: experimentation-triptych +:width: 100% +:align: center + +The experimentation lifecycle as a Bosch triptych. *Left, Bayesian Assurance:* before any data arrive, the planner reads possible effects from the prior and asks what the experiment will likely conclude. *Centre, Sensitivity Analysis (this notebook):* a single experiment is wracked by the biases it cannot rule out, and the model is contorted to see which commitments its conclusion can survive. *Right, Meta-Analysis:* many experiments are pooled through a hierarchy of levels into a synthesis that becomes the next plan's prior. Three panels, one posterior machinery. +::: + +All applied inference is argument. Against every experiment you can set the contention that the working conditions were imperfect. Some aspect of the evaluation was flawed. Maybe treatment assignment introduced a subtle kind of bias, or the subjects didn't comply fully with the design. Against every experiment you can contrast the scientific ideal of perfect randomisation and clear adherence. Holding an experiment against that ideal is due diligence. Sensitivity analysis does it systematically, by varying how far the working conditions fall short of perfect randomisation. + +## The randomisation gap + +Randomisation is an assumption you maintain by design, not a fact you assert by intention. The checkout experiment ran, the headline effect on revenue-per-visitor looks positive, and somewhere in the diagnostic notes there is a line about compliance being 73%: users on slow connections were silently routed back to the old flow by a CDN edge case, and the routing was not random in the way it touched the population. The intent-to-treat estimate now depends on a counterfactual the experiment did not produce: what those users would have done under the new flow. Without further assumptions, the data cannot say what the treatment effect would have been if randomisation had held. + +This notebook develops the Bayesian response to this situation. Where Rosenbaum's $\Gamma$ {cite:p}`rosenbaum2002observational` and the E-value {cite:p}`vanderweele2017sensitivity` give point summaries of how strong an unmeasured confounder would need to be to nullify the result, the Bayesian framing makes the same unmeasured confounder a *parameter* in the model, with a prior over its plausible strength and a posterior shaped by both the data and the analyst's commitments {cite:p}`imbens2003sensitivity`, {cite:p}`cinellihazlett2020omitted`. We develop the machinery on a continuous outcome (revenue per visitor) and then re-run it on a binary outcome (conversion). This is the second of three notebooks on the lifecycle of a Bayesian experiment; see {ref}`assurance_planning` for the planning counterpart and {ref}`meta_analysis_experiments` for the synthesis counterpart. The clean primary analysis of a well-run experiment, the posterior on the effect with the decision rule applied, appears as the demonstration step in {ref}`assurance_planning`; this notebook takes up the interpretation once that clean identification is itself in question. + +:::{admonition} Where this lands in regulatory practice +:class: note + +The sensitivity construction here follows the regulatory recommendation directly. The FDA's 2026 draft guidance on Bayesian methodology in clinical trials describes sensitivity analysis as varying the prior over a critical assumption, and notes that "some approaches can build uncertainty about specific assumptions into the prior itself" {cite:p}`fda2026bayesian`, which is the move made below. The guidance goes further and sanctions modelling a discrepancy between data sources with "an assumed bias parameter in the model", the exact object this notebook places a prior on and sweeps. The clinical-trial setting differs from a product quasi-experiment; the bias parameter is the same. +::: + +```{code-cell} ipython3 +import warnings + +import arviz as az +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +import pymc as pm + +warnings.filterwarnings("ignore", category=RuntimeWarning) +warnings.filterwarnings("ignore", category=UserWarning) +``` + +```{code-cell} ipython3 +%config InlineBackend.figure_format = 'retina' +az.style.use("arviz-variat") +rng = np.random.default_rng(7) +RANDOM_SEED = 7 +``` + +## What the data can and cannot say + +The structural picture is small and the notation traditional. Let $T$ be the observed treatment indicator (which flow the visitor actually saw), let $Y$ be the outcome (revenue), and let $U$ be an unmeasured user characteristic: connection quality, engagement disposition, whatever drives the differential compliance. Under randomisation $U$ is independent of $T$ by construction; under compliance failure $U$ is associated with $T$ and unobservable. + +```{code-cell} ipython3 +:tags: [hide-input] + +fig, ax = plt.subplots(figsize=(15, 3.5)) +ax.set_xlim(0, 10) +ax.set_ylim(0, 5) +ax.axis("off") + +nodes = {"T": (2, 1.5), "Y": (8, 1.5), "U": (5, 4)} +for name, (x, y) in nodes.items(): + ax.scatter(x, y, s=2200, facecolor="white", edgecolor="black", zorder=3) + ax.text(x, y, name, ha="center", va="center", fontsize=16, zorder=4) + + +def arrow(a, b, **kw): + (x0, y0), (x1, y1) = nodes[a], nodes[b] + ax.annotate( + "", + xy=(x1, y1), + xytext=(x0, y0), + arrowprops=dict(arrowstyle="->", lw=2, shrinkA=22, shrinkB=22, **kw), + ) + + +arrow("T", "Y") +arrow("U", "T", color="firebrick") +arrow("U", "Y", color="firebrick") + +ax.text(5, 1.8, r"$\tau$ (causal effect)", ha="center", fontsize=11) +ax.text(3.2, 3.3, r"$\lambda_T$", color="firebrick", fontsize=12) +ax.text(6.8, 3.3, r"$\lambda_Y$", color="firebrick", fontsize=12) +ax.set_title("The identification gap: $U$ unobserved", fontsize=12); +``` + +What we want is $\tau$, the causal effect of $T$ on $Y$. What the data identify is $\tau$ *plus* the contribution of any path that flows through $U$: the product of the two red edges, collected into a single bias term $\beta = \lambda_T \cdot \lambda_Y / \mathrm{var}(T)$ at the scale of the observed difference in means {cite:p}`hernan2020whatif`, {cite:p}`cunningham2021causal`. The naïve estimator returns $\tau + \beta$. The data are silent on the decomposition; the prior is what sets it. + +## The bias parameter + +The Bayesian sensitivity analysis makes $\beta$ a model parameter with a prior. The data inform the sum $\tau + \beta$ through the observed difference; the prior on $\beta$ controls how much of that sum is attributed to the unmeasured confounder rather than to the treatment. Three prior commitments: + +- **Dismissive prior** ($\beta \sim \mathcal{N}(0, 0.05)$): "I am confident there is essentially no confounding." +- **Moderate prior** ($\beta \sim \mathcal{N}(0, 0.3)$): "I will allow that confounding may have shifted the apparent effect by up to a few tenths of a revenue unit." +- **Sceptical prior** ($\beta \sim \mathcal{N}(0, 0.7)$): "I will not commit to confounding being small; the data must speak loudly to be heard." + +Each is an auditable commitment. + +```{code-cell} ipython3 +N = 4000 +TRUE_TAU = 0.30 +TRUE_BIAS = 0.50 +SIGMA_OBS = 4.0 + + +def simulate_quasi_experimental_gaussian(N, true_tau, true_bias, sigma_obs, rng): + baseline = 10.0 + y_A = rng.normal(baseline, sigma_obs, size=N) + y_B = rng.normal(baseline + true_tau + true_bias, sigma_obs, size=N) + return y_A, y_B + + +y_A_obs, y_B_obs = simulate_quasi_experimental_gaussian(N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, rng) +d_hat = y_B_obs.mean() - y_A_obs.mean() +sigma_d = np.sqrt(2 * SIGMA_OBS**2 / N) +print(f"Observed difference d_hat = {d_hat:.3f} (sampling SE = {sigma_d:.3f})") +print(f"True tau = {TRUE_TAU}, true bias = {TRUE_BIAS}, true sum = {TRUE_TAU + TRUE_BIAS}") +``` + +The observed difference recovers the *biased* effect, as it must. $\tau$ is what we want; $\beta$ is what we cannot observe. Before asking how a prior reshapes that sum, confirm the machinery is faithful: hand the model the belief an analyst would hold if they knew the confounder exactly, a prior on $\beta$ centred at the true bias, and the treatment effect should return unbiased across repeated experiments. + +```{code-cell} ipython3 +def gaussian_sensitivity_posterior( + d_hat, sigma_d, tau_prior_sd, bias_prior_sd, tau_prior_mean=0.0, bias_prior_mean=0.0 +): + """Closed-form posterior over (tau, beta) given the observed effect.""" + prior_precision = np.diag([1.0 / tau_prior_sd**2, 1.0 / bias_prior_sd**2]) + F = np.array([[1.0, 1.0]]) + data_precision = F.T @ F / sigma_d**2 + post_precision = prior_precision + data_precision + post_cov = np.linalg.inv(post_precision) + prior_mean = np.array([tau_prior_mean, bias_prior_mean]) + rhs = prior_precision @ prior_mean + F.flatten() * d_hat / sigma_d**2 + post_mean = post_cov @ rhs + return post_mean, post_cov + + +# Across many synthetic quasi-experiments, where does the posterior mean of tau land +# when the analyst's prior on the bias is centred at the true confounding strength? +recovery_rng = np.random.default_rng(RANDOM_SEED) +n_recovery = 500 +tau_posterior_means = np.empty(n_recovery) +for i in range(n_recovery): + y_A_i, y_B_i = simulate_quasi_experimental_gaussian( + N, TRUE_TAU, TRUE_BIAS, SIGMA_OBS, recovery_rng + ) + d_hat_i = y_B_i.mean() - y_A_i.mean() + post_mean_i, _ = gaussian_sensitivity_posterior( + d_hat_i, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.1, bias_prior_mean=TRUE_BIAS + ) + tau_posterior_means[i] = post_mean_i[0] + +fig, ax = plt.subplots(figsize=(20, 4)) +ax.hist(tau_posterior_means, bins=30, color="C0", alpha=0.7, edgecolor="white") +ax.axvline(TRUE_TAU, color="C2", linestyle="--", linewidth=2, label=f"true \u03c4 = {TRUE_TAU:.2f}") +ax.axvline( + tau_posterior_means.mean(), + color="C3", + linewidth=2, + label=f"mean estimate = {tau_posterior_means.mean():.3f}", +) +ax.set_xlabel(r"Posterior mean of $\tau$ across simulated experiments") +ax.set_ylabel("Frequency") +ax.set_title(r"Recovery of $\tau$ when the bias prior is correctly centred") +ax.legend(); +``` + +The sampling distribution of the posterior mean sits on the true $\tau = 0.30$: with the confounder's strength correctly specified, the estimator is unbiased across repeated experiments. The recovery is real, but read what produced it. The data fixed the sum $\tau + \beta$ through the observed difference; the correctly-centred prior on $\beta$ is what split that sum into its parts. A single difference in means cannot separate a treatment effect from a confound that imitates it. The data identify the two only in combination with a commitment about the confounder. The prior is the content of that decomposition, which is why an honest analysis varies it rather than fixing it. Recentre the prior on $\beta$ at zero, where an analyst lands by default with no oracle for the confounder's size, and the estimate moves. The moderate prior below makes the shift concrete. + +```{code-cell} ipython3 +def gaussian_sensitivity_model(d_hat, sigma_d, tau_prior=(0.0, 1.0), bias_prior=(0.0, 0.3)): + with pm.Model() as model: + tau = pm.Normal("tau", mu=tau_prior[0], sigma=tau_prior[1]) + beta = pm.Normal("beta", mu=bias_prior[0], sigma=bias_prior[1]) + observed_effect = pm.Deterministic("observed_effect", tau + beta) + pm.Normal("d_hat", mu=observed_effect, sigma=sigma_d, observed=d_hat) + return model + + +with gaussian_sensitivity_model(d_hat, sigma_d, bias_prior=(0.0, 0.3)): + idata_moderate = pm.sample( + draws=2000, + tune=2000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) + +az.plot_dist(idata_moderate, var_names=["tau", "beta"]) +axes = plt.gcf().axes +for a in axes: + a.set_title("") +axes[0].axvline(TRUE_TAU, color="C2", linestyle="--", label=f"true τ = {TRUE_TAU:.2f}") +axes[0].legend() +axes[1].axvline(TRUE_BIAS, color="C2", linestyle="--", label=f"true β = {TRUE_BIAS:.2f}") +axes[1].legend() +plt.suptitle(r"Posterior of $\tau$ and $\beta$ under a moderate bias prior"); +``` + +Under the moderate prior, centred at zero, the posterior of $\tau$ is pulled well above the true 0.30 and the posterior of $\beta$ settles near zero: with no prior reason to expect a confounder, the treatment absorbs the sum. The true $\beta = 0.50$ falls in the prior's right tail. The data informed the sum; the prior shaped the split. + +### Tipping-point analysis under a Gaussian outcome + +The model with a flat prior on $\tau$ and a Gaussian prior on $\beta$ is fully conjugate; the posterior is a closed-form bivariate Normal that we can compute analytically. This lets us trace the tipping point: the bias prior strength at which the posterior probability of a positive treatment effect drops below the team's decision threshold. + +```{code-cell} ipython3 +# Verify the closed form agrees with MCMC under the moderate prior +post_mean_anly, post_cov_anly = gaussian_sensitivity_posterior( + d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=0.3 +) +mcmc_summary = az.summary(idata_moderate, var_names=["tau", "beta"], kind="stats")[["mean", "sd"]] +analytical_summary = pd.DataFrame( + {"mean": post_mean_anly, "sd": np.sqrt(np.diag(post_cov_anly))}, + index=["tau", "beta"], +) +pd.concat({"MCMC": mcmc_summary, "Analytical": analytical_summary}, axis=1).round(3) +``` + +The two posteriors agree. The analytical form carries the sweep. + +```{code-cell} ipython3 +from scipy import stats + +bias_sd_grid = np.linspace(0.001, 1.0, 40) +sweep_records = [] +for bias_sd in bias_sd_grid: + pm_a, pc_a = gaussian_sensitivity_posterior( + d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=bias_sd + ) + tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0]) + prob_positive = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd) + sweep_records.append( + {"bias_sd": bias_sd, "tau_mean": tau_mean, "tau_sd": tau_sd, "prob_positive": prob_positive} + ) +sweep_df = pd.DataFrame(sweep_records) + +decision_threshold = 0.95 +above_threshold = sweep_df[sweep_df["prob_positive"] >= decision_threshold] +tipping_point = above_threshold["bias_sd"].max() if len(above_threshold) else np.nan + +fig, axes = plt.subplots(1, 2, figsize=(20, 4)) +axes[0].plot( + sweep_df["bias_sd"], + sweep_df["tau_mean"], + linewidth=2, + color="C0", + label=r"Posterior mean of $\tau$", +) +axes[0].fill_between( + sweep_df["bias_sd"], + sweep_df["tau_mean"] - sweep_df["tau_sd"], + sweep_df["tau_mean"] + sweep_df["tau_sd"], + alpha=0.25, + color="C0", + label=r"$\pm 1$ SD", +) +axes[0].axhline(0.0, color="black", linestyle=":") +axes[0].set_xlabel(r"Prior SD on bias $\beta$") +axes[0].set_ylabel(r"Posterior of $\tau$") +axes[0].set_title("Posterior shifts as the bias prior loosens") +axes[0].legend() + +axes[1].plot(sweep_df["bias_sd"], sweep_df["prob_positive"], linewidth=2, color="C3") +axes[1].axhline( + decision_threshold, + color="black", + linestyle="--", + label=f"Decision threshold = {decision_threshold}", +) +if not np.isnan(tipping_point): + axes[1].axvline( + tipping_point, + color="C3", + linestyle=":", + alpha=0.7, + label=f"Tipping point ≈ {tipping_point:.2f}", + ) +axes[1].set_xlabel(r"Prior SD on bias $\beta$") +axes[1].set_ylabel(r"$P(\tau > 0 \mid d_{\text{obs}})$") +axes[1].set_title("Tipping point in the decision rule") +axes[1].legend(); +``` + +Read the left panel from left to right: as the analyst loosens their prior on the bias, the posterior mean of $\tau$ drifts downward and the posterior interval widens. Read the right panel: there is a bias prior strength at which the posterior probability of a positive effect falls below the conventional decision threshold. The tipping point is a price tag on the claim rather than a refutation of the experiment. To assert a positive effect requires a stated belief that the bias prior is *tighter* than the tipping point. The honest version of the conversation with stakeholders runs through this number. The posterior is what makes that conversation possible: the same inference machinery that reads the experiment's results in a clean world is what traces the contour of its fragility here. The question has shifted from what the treatment did to which commitments about the unmeasured bias are needed to believe it did anything, and a posterior answers the new question as readily as the old. + +The same machinery runs on the log-odds scale. Before mapping the full topology of the bias-prior space, we confirm that the one-dimensional fragility picture is not an artefact of the Gaussian likelihood. + ++++ + +## The same machinery on a binary outcome + +The conversion-rate version of the experiment uses the same structural model on the log-odds scale. The bias parameter now lives on the logit, but the framing is identical: the observed log-odds difference is the sum of a treatment effect and an unmeasured-confounder contribution, and a prior over the latter is the only thing that separates them. + +```{code-cell} ipython3 +def simulate_quasi_experimental_bernoulli(N, baseline_rate, true_tau_logit, true_bias_logit, rng): + from scipy.special import expit + + p_A = expit(np.log(baseline_rate / (1 - baseline_rate))) + p_B = expit(np.log(baseline_rate / (1 - baseline_rate)) + true_tau_logit + true_bias_logit) + n_A = rng.binomial(N, p_A) + n_B = rng.binomial(N, p_B) + return n_A, n_B, p_A, p_B + + +BASELINE_RATE_B = 0.10 +TRUE_TAU_LOGIT = 0.15 +TRUE_BIAS_LOGIT = 0.30 + +n_A_obs, n_B_obs, p_A_true, p_B_true = simulate_quasi_experimental_bernoulli( + N=8000, + baseline_rate=BASELINE_RATE_B, + true_tau_logit=TRUE_TAU_LOGIT, + true_bias_logit=TRUE_BIAS_LOGIT, + rng=rng, +) +print(f"Observed conversions: A = {n_A_obs}/8000, B = {n_B_obs}/8000") +print(f"True p_A = {p_A_true:.4f}, p_B (with bias) = {p_B_true:.4f}") +``` + +```{code-cell} ipython3 +def bernoulli_sensitivity_model( + n_A, n_B, N, baseline_logit_prior=(-2.0, 0.5), tau_prior=(0.0, 0.5), bias_prior=(0.0, 0.3) +): + with pm.Model() as model: + logit_p_A = pm.Normal( + "logit_p_A", mu=baseline_logit_prior[0], sigma=baseline_logit_prior[1] + ) + tau = pm.Normal("tau", mu=tau_prior[0], sigma=tau_prior[1]) + beta = pm.Normal("beta", mu=bias_prior[0], sigma=bias_prior[1]) + logit_p_B = pm.Deterministic("logit_p_B", logit_p_A + tau + beta) + p_A = pm.Deterministic("p_A", pm.math.invlogit(logit_p_A)) + p_B = pm.Deterministic("p_B", pm.math.invlogit(logit_p_B)) + pm.Binomial("obs_A", n=N, p=p_A, observed=n_A) + pm.Binomial("obs_B", n=N, p=p_B, observed=n_B) + return model + + +tipping_records_bern = [] +for bias_sd in [0.05, 0.15, 0.2, 0.30, 0.50, 0.80]: + with bernoulli_sensitivity_model(n_A_obs, n_B_obs, N=8000, bias_prior=(0.0, bias_sd)): + idata = pm.sample( + draws=1000, + tune=1000, + chains=2, + target_accept=0.95, + random_seed=RANDOM_SEED, + progressbar=False, + ) + tau_samples = idata.posterior["tau"].values.flatten() + tipping_records_bern.append( + { + "bias_sd": bias_sd, + "tau_mean": tau_samples.mean(), + "tau_sd": tau_samples.std(), + "prob_positive": float((tau_samples > 0).mean()), + } + ) +tipping_bern_df = pd.DataFrame(tipping_records_bern) +# prob_positive decreases as the bias prior loosens; interpolate to the threshold crossing +tip_bern = float( + np.interp( + decision_threshold, + tipping_bern_df["prob_positive"].values[::-1], + tipping_bern_df["bias_sd"].values[::-1], + ) +) +tipping_bern_df.round(3) +``` + +```{code-cell} ipython3 +fig, axes = plt.subplots(1, 2, figsize=(20, 4)) +axes[0].errorbar( + tipping_bern_df["bias_sd"], + tipping_bern_df["tau_mean"], + yerr=tipping_bern_df["tau_sd"], + marker="o", + linewidth=2, + capsize=4, +) +axes[0].axhline(0.0, color="black", linestyle=":") +axes[0].set_xlabel(r"Prior SD on bias $\beta$ (log-odds)") +axes[0].set_ylabel(r"Posterior of $\tau$ (log-odds)") +axes[0].set_title("Bernoulli case: posterior of treatment effect") + +axes[1].plot( + tipping_bern_df["bias_sd"], + tipping_bern_df["prob_positive"], + marker="o", + linewidth=2, + color="C3", +) +axes[1].axhline( + decision_threshold, + color="black", + linestyle="--", + label=f"Decision threshold = {decision_threshold}", +) +axes[1].axvline( + tip_bern, + color="C3", + linestyle=":", + alpha=0.7, + label=f"Tipping point ≈ {tip_bern:.2f}", +) +axes[1].set_xlabel(r"Prior SD on bias $\beta$ (log-odds)") +axes[1].set_ylabel(r"$P(\tau > 0 \mid \text{data})$") +axes[1].set_title("Tipping point on the log-odds scale") +axes[1].legend(); +``` + +The shape of the curve confirms what the Gaussian case showed: the decision rule loses confidence as the prior on bias widens, and the tipping point is identifiable on the log-odds scale just as it was on the revenue scale. The E-value of {cite:p}`vanderweele2017sensitivity` corresponds, roughly, to the bias magnitude at which a frequentist decision would tip; the Bayesian curve is the full posterior over that commitment. One dimension, two likelihoods, the same fragility picture. The complete audit needs both dimensions of the bias prior, the full region of commitments the conclusion can survive. That surface is below. + ++++ + +### The sensitivity surface + +Both the Gaussian and the binary sweep moved one dimension of the bias prior. The complete audit requires the other: a map of the full region of $(\mu_\beta, \sigma_\beta)$ commitments the experiment can survive. The sweep below opens the line into a surface. + +```{code-cell} ipython3 +bias_mu_grid = np.linspace(-0.5, 0.5, 25) +bias_sd_grid_2d = np.linspace(0.01, 1.0, 25) +prob_grid = np.zeros((len(bias_sd_grid_2d), len(bias_mu_grid))) + +for i, b_sd in enumerate(bias_sd_grid_2d): + for j, b_mu in enumerate(bias_mu_grid): + pm_a, pc_a = gaussian_sensitivity_posterior( + d_hat, sigma_d, tau_prior_sd=1.0, bias_prior_sd=b_sd, bias_prior_mean=b_mu + ) + tau_mean, tau_sd = pm_a[0], np.sqrt(pc_a[0, 0]) + prob_grid[i, j] = 1.0 - stats.norm.cdf(0.0, loc=tau_mean, scale=tau_sd) + +fig, ax = plt.subplots(figsize=(15, 5)) +im = ax.imshow( + prob_grid, + origin="lower", + aspect="auto", + extent=[bias_mu_grid.min(), bias_mu_grid.max(), bias_sd_grid_2d.min(), bias_sd_grid_2d.max()], + cmap="RdBu_r", + vmin=0.0, + vmax=1.0, +) +contour = ax.contour( + bias_mu_grid, + bias_sd_grid_2d, + prob_grid, + levels=[0.5, decision_threshold], + colors=["white", "black"], + linewidths=[1.2, 2.0], +) +ax.clabel(contour, fmt={0.5: "P=0.5", decision_threshold: f"P={decision_threshold}"}) +ax.set_xlabel(r"Prior mean of bias $\beta$") +ax.set_ylabel(r"Prior SD of bias $\beta$") +ax.set_title(r"$P(\tau > 0)$ under bias-prior commitments") +plt.colorbar(im, ax=ax, label=r"$P(\tau > 0 \mid d_{\text{obs}})$"); +``` + +The decision threshold contour partitions the bias-prior plane into a region where the experiment is defensible and a region where it is not. The analyst who wants to claim a positive effect commits to a point inside the inner contour. The dissenter who wants to claim the effect is artefactual commits to a point outside it. The graph locates the disagreement rather than settling it. It shows which region of the bias-prior plane each party's commitments occupy, and whether that region sits inside or outside the contour of defensibility. The audit has a legible geometry. + ++++ + +## Robustness as a posterior question + +A sensitivity analysis maps the randomisation gap rather than closing it. The sweep above does not prove the experiment robust; it produces an auditable exhibit of which bias commitments the experiment can survive and which it cannot. That exhibit is the deliverable. + +This changes what honest reporting looks like. The headline from a quasi-experiment becomes the *tipping point*, the prior on the bias at which the conclusion turns, and the sensitivity surface widens that point into a region: the full set of bias-prior commitments the experiment can survive, with its boundary drawn as a contour. Two analysts who hold the same data and reach opposite conclusions are reading the same difference in means through different priors on the confounder, and the surface shows precisely which commitment divides them. + +What a clean experiment reports as one posterior on the effect, a quasi-experiment reports as a posterior spread over the bias the data cannot rule out. Mapping that spread, and naming the commitment a positive conclusion requires, is what the quasi-experiment owes its readers. {ref}`meta_analysis_experiments` turns from a single threatened experiment to a whole series of them. + +## Authors + +- Authored by [Nathaniel Forde](https://nathanielf.github.io/) in May 2026. + +## References + +:::{bibliography} +:filter: docname in docnames +::: + +## Watermark + +```{code-cell} ipython3 +%load_ext watermark +%watermark -n -u -v -iv -w -p pytensor,xarray +``` + +:::{include} ../page_footer.md +::: diff --git a/examples/references.bib b/examples/references.bib index bf45cc5d1..e5a8f246c 100644 --- a/examples/references.bib +++ b/examples/references.bib @@ -102,6 +102,12 @@ @article{bonilla2007multioutput year = {2007}, url = {https://papers.nips.cc/paper/2007/hash/66368270ffd51418ec58bd793f2d9b1b-Abstract.html} } +@book{borenstein2009meta, + title = {Introduction to Meta-Analysis}, + author = {Borenstein, Michael and Hedges, Larry V. and Higgins, Julian P. T. and Rothstein, Hannah R.}, + year = {2009}, + publisher = {John Wiley \& Sons} +} @book{breen1996regression, title = {Regression models: Censored, sample selected, or truncated data}, author = {Breen, Richard and others}, @@ -164,6 +170,16 @@ @article{ChernozhukovDoubleML year = {2018}, doi = {https://doi.org/10.1111/ectj.12097} } +@article{cinellihazlett2020omitted, + title = {Making sense of sensitivity: extending omitted variable bias}, + author = {Cinelli, Carlos and Hazlett, Chad}, + journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, + volume = {82}, + number = {1}, + pages = {39--67}, + year = {2020}, + doi = {10.1111/rssb.12348} +} @book{coles2001gev, title = {An introduction to statistical modeling of extreme values}, author = {Coles, Stuart}, @@ -253,12 +269,30 @@ @book{enders2022 year = {2022}, publisher = {The Guilford Press} } +@article{evans2006checking, + title = {Checking for prior-data conflict}, + author = {Evans, Michael and Moshonov, Hadas}, + journal = {Bayesian Analysis}, + volume = {1}, + number = {4}, + pages = {893--914}, + year = {2006} +} @book{facure2023causal, title = {Causal Inference in Python}, author = {Facure, Matheus}, year = {2023}, publisher = {O'Reilly} } +@techreport{fda2026bayesian, + title = {Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products: Guidance for Industry (Draft Guidance)}, + author = {{U.S. Food and Drug Administration}}, + institution = {Center for Drug Evaluation and Research (CDER) and Center for Biologics Evaluation and Research (CBER)}, + type = {Draft Guidance}, + year = {2026}, + month = jan, + note = {Distributed for comment purposes only} +} @book{fox2010bayesian, title = {Bayesian item response modeling: Theory and applications}, author = {Fox, Jean-Paul}, @@ -373,6 +407,16 @@ @book{hernan2020whatif year = {2020}, publisher = {Chapman \& Hall/CRC} } +@article{higgins2009meta, + title = {A re-evaluation of random-effects meta-analysis}, + author = {Higgins, Julian P. T. and Thompson, Simon G. and Spiegelhalter, David J.}, + journal = {Journal of the Royal Statistical Society: Series A (Statistics in Society)}, + volume = {172}, + number = {1}, + pages = {137--159}, + year = {2009}, + doi = {10.1111/j.1467-985X.2008.00552.x} +} @article{hoffman2014nuts, title = {The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo}, author = {Hoffman, Matthew and Gelman, Andrew}, @@ -441,6 +485,25 @@ @article{iacobucci2017mean year = {2017}, publisher = {Springer} } +@article{ibrahim2000power, + title = {Power prior distributions for regression models}, + author = {Ibrahim, Joseph G. and Chen, Ming-Hui}, + journal = {Statistical Science}, + volume = {15}, + number = {1}, + pages = {46--60}, + year = {2000} +} +@article{imbens2003sensitivity, + title = {Sensitivity to exogeneity assumptions in program evaluation}, + author = {Imbens, Guido W.}, + journal = {American Economic Review}, + volume = {93}, + number = {2}, + pages = {126--132}, + year = {2003}, + doi = {10.1257/000282803321946921} +} @book{ivezić2014astroMLtext, author = {\v{Z}eljko Ivezi\'{c} and Andrew J. Connolly and Jacob T. VanderPlas and Alexander Gray}, doi = {10.1515/9781400848911}, @@ -731,16 +794,16 @@ @online{numpyroBirthdays title = {Example: Hilbert space approximation for Gaussian processes}, url = {https://num.pyro.ai/en/stable/examples/hsgp.html} } -@online{numpyroBirthdays, - title = {Example: Hilbert space approximation for Gaussian processes}, - url = {https://num.pyro.ai/en/stable/examples/hsgp.html} -} -@online{orduz2024Birthdays, - title = {Time Series Modeling with HSGP: Baby Births Example}, - author = {Orduz, Juan}, - url = {https://juanitorduz.github.io/birthdays/}, - urldate = {2024-01-02}, - year = {2024} +@article{ohagan2005assurance, + title = {Assurance in clinical trial design}, + author = {O'Hagan, Anthony and Stevens, John W. and Campbell, Michael J.}, + journal = {Pharmaceutical Statistics}, + volume = {4}, + number = {3}, + pages = {187--201}, + year = {2005}, + publisher = {Wiley Online Library}, + doi = {10.1002/pst.175} } @online{orduz2024Birthdays, title = {Time Series Modeling with HSGP: Baby Births Example}, @@ -808,21 +871,6 @@ @article{penrose1985 year = {1985}, pages = {189} } -@article{penrose1985, - title = {{GENERALIZED} {BODY} {COMPOSITION} {PREDICTION} {EQUATION} {FOR} {MEN} {USING} {SIMPLE} {MEASUREMENT} {TECHNIQUES}}, - volume = {17}, - issn = {0195-9131}, - url = {https://journals.lww.com/acsm-msse/citation/1985/04000/generalized_body_composition_prediction_equation.37.aspx}, - abstract = {An abstract is unavailable. This article is available as a PDF only.}, - language = {en-US}, - number = {2}, - urldate = {2023-10-17}, - journal = {Medicine \& Science in Sports \& Exercise}, - author = {Penrose, K. W. and Nelson, A. G. and Fisher, A. G.}, - month = apr, - year = {1985}, - pages = {189} -} @misc{quiroga2022bart, title = {Bayesian additive regression trees for probabilistic programming}, author = {Quiroga, Miriana and Garay, Pablo G and Alonso, Juan M. and Loyola, Juan Martin and Martin, Osvaldo A}, @@ -862,17 +910,6 @@ @article{riutort2022PracticalHilbertSpaceApproximate volume = {33}, year = {2022} } -@article{riutort2022PracticalHilbertSpaceApproximate, - author = {Riutort-Mayol, Gabriel and B{\"u}rkner, Paul-Christian and Andersen, Michael R. and Solin, Arno and Vehtari, Aki}, - doi = {10.1007/s11222-022-10167-2}, - journal = {Statistics and Computing}, - number = {1}, - pages = {17}, - title = {Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming}, - url = {https://doi.org/10.1007/s11222-022-10167-2}, - volume = {33}, - year = {2022} -} @book{roback2021beyond, title = {Beyond multiple linear regression: Applied generalized linear models and multilevel models in R}, author = {Roback, P., and Legler, J.}, @@ -884,6 +921,13 @@ @online{rochford2018 author = {Austin Rochford}, url = {https://austinrochford.com/posts/2018-11-10-monotonic-predictors.html} } +@book{rosenbaum2002observational, + title = {Observational Studies}, + author = {Rosenbaum, Paul R.}, + year = {2002}, + publisher = {Springer}, + edition = {2nd} +} @book{rousseeuw2005robust, author = {Rousseeuw, Peter J. and Leroy, Annick M.}, title = {Robust Regression and Outlier Detection}, @@ -892,6 +936,16 @@ @book{rousseeuw2005robust year = {2005}, isbn = {978-0-471-48855-2} } +@incollection{rubin1981estimation, + title = {Estimation in parallel randomized experiments}, + author = {Rubin, Donald B.}, + journal = {Journal of Educational Statistics}, + volume = {6}, + number = {4}, + pages = {377--401}, + year = {1981}, + doi = {10.3102/10769986006004377} +} @misc{säilynoja2025, title = {Recommendations for visual predictive checks in Bayesian workflow}, author = {Teemu S\"{a}ilynoja and Andrew R. Johnson and Osvaldo A. Martin and Aki Vehtari}, @@ -940,16 +994,11 @@ @article{solin2020Hilbert volume = {30}, year = {2020} } -@article{solin2020Hilbert, - author = {Solin, Arno and S{\"a}rkk{\"a}, Simo}, - doi = {10.1007/s11222-019-09886-w}, - journal = {Statistics and Computing}, - number = {2}, - pages = {419--446}, - title = {Hilbert space methods for reduced-rank Gaussian process regression}, - url = {https://doi.org/10.1007/s11222-019-09886-w}, - volume = {30}, - year = {2020} +@book{spiegelhalter2004bayesian, + title = {Bayesian Approaches to Clinical Trials and Health-Care Evaluation}, + author = {Spiegelhalter, David J. and Abrams, Keith R. and Myles, Jonathan P.}, + year = {2004}, + publisher = {John Wiley \& Sons} } @article{spiller2013spotlights, title = {Spotlights, floodlights, and the magic number zero: Simple effects tests in moderated regression}, @@ -1040,6 +1089,16 @@ @inproceedings{vanderplas2012astroML doi = {10.1109/CIDU.2012.6382200}, year = {2012} } +@article{vanderweele2017sensitivity, + title = {Sensitivity analysis in observational research: introducing the {E}-value}, + author = {VanderWeele, Tyler J. and Ding, Peng}, + journal = {Annals of Internal Medicine}, + volume = {167}, + number = {4}, + pages = {268--274}, + year = {2017}, + doi = {10.7326/M16-2607} +} @book{vehkalahti2019multivariate, title = {Multivariate Analysis for the Behavioral Sciences}, author = {Vehkalahti, K. and Everitt, B.S.}, @@ -1055,13 +1114,6 @@ @online{vehtari2022Birthdays urldate = {2022-03-07}, year = {2022} } -@online{vehtari2022Birthdays, - title = {Bayesian workflow book - Birthdays}, - author = {Vehtari, Aki}, - url = {https://avehtari.github.io/casestudies/Birthdays/birthdays.html}, - urldate = {2022-03-07}, - year = {2022} -} @book{venables2002mass, author = {Venables, W. N. and Ripley, B. D.}, title = {Modern Applied Statistics with {S}}, @@ -1132,19 +1184,6 @@ @article{Yao_2022 doi = {10.1214/21-BA1287}, url = {https://doi.org/10.1214/21-BA1287} } -@article{Yao_2022, - author = {Yuling Yao and Gregor Pir\v{s} and Aki Vehtari and Andrew Gelman}, - title = {{Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful}}, - volume = {17}, - journal = {Bayesian Analysis}, - number = {4}, - publisher = {International Society for Bayesian Analysis}, - pages = {1043 -- 1071}, - keywords = {Bayesian hierarchical modeling, conditional prediction, covariate shift, model averaging, prior construction, stacking}, - year = {2022}, - doi = {10.1214/21-BA1287}, - url = {https://doi.org/10.1214/21-BA1287} -} @article{yuan2009bayesian, title = {Bayesian mediation analysis.}, author = {Yuan, Ying and MacKinnon, David P}, diff --git a/pixi.toml b/pixi.toml index 284d50ac4..9eaca3712 100644 --- a/pixi.toml +++ b/pixi.toml @@ -3,19 +3,19 @@ authors = ["Chris Fonnesbeck "] channels = ["conda-forge"] description = "Add a short description here" name = "pymc-examples" -platforms = ["linux-64"] +platforms = ["linux-64", "osx-arm64"] version = "0.1.0" [tasks] [dependencies] python = ">=3.13.9,<3.14" -pymc = ">=5.26.1,<6" +pymc = ">=6.0,<7" jupyter = ">=1.1.1,<2" ipykernel = ">=7.1.0,<8" ipywidgets = ">=8.1.8,<9" numpy = ">=2.3.5,<3" -arviz = ">=0.22.0,<0.23" +arviz = ">=1.0,<2" numpyro = ">=0.19.0,<0.20" seaborn = ">=0.13.2,<0.14" matplotlib = ">=3.10.8,<4"