CSMC for Diffusions

This repository contains the code and scripts required to replicate the experimental result of "Inference for Diffusion Processes via Controlled Sequential Monte Carlo and Splitting Schemes" by S. Huang,1 R. G. Everitt, M. Tamborrino and A. M. Johansen.

It includes an R package implementing the core algorithms and a collection of scripts for reproducing all displayed results.

Adaptive_SPSA Scripts

Purpose:

Reproduce the point estimates for simulated FHN data that gives the density plots (Fig. 4 and 7) .

Scripts:

1. bridge_4_005_LT.r
   • What it does: For a given seed, simulates FHN data and maximizes the 4-step bridged Lie-Trotter partial likelihood using SPSA\
   • Customise: Set seed number (Line 982)\
   • Output: Numerical matrix of full convergence trajectory
2. bridge_4_005_S.r
   • What it does: For a given seed, simulates FHN data and maximizes the 4-step bridged Strang partial likelihood using SPSA\
   • Customise: Set seed number (Line 1003)\
   • Output: Numerical matrix of full convergence trajectory
3. bridge_8_005_LT.r
   • What it does: For a given seed, simulates FHN data and maximizes the 8-step bridged Lie-Trotter partial likelihood using SPSA\
   • Customise: Set seed number (Line 982)\
   • Output: Numerical matrix of full convergence trajectory
4. bridge_8_005_S.r
   • What it does: For a given seed, simulates FHN data and maximizes the 8-step bridged Strang partial likelihood using SPSA\
   • Customise: Set seed number (Line 1004)\
   • Output: Numerical matrix of full convergence trajectory

Execution:

• Each script is independent
• Was run with seeds 1-100 for full results

cSMC Package

Purpose:

Contains the installable R package (cSMC) implementing a very basic cSMC; it is required for the MCMC and application script.

Installation:

1. Open cSMC.Rproj in RStudio
2. Install the package in the Build interface

MCMC Scripts

Purpose:

Reproduce the posterior density plot (Fig. 3) for simulated FHN data.

Dependencies

• mvnfast, MASS, mvtnorm, cSMC

Scripts:

1. BPF_mcmc.R
   • What it does: Produces result corresponds to the red line of Fig. 3
   • Output: Numerical matrix containing the full BPF-PMMH trajectory
2. cSMC_mcmc.R
   • What it does: Produces result corresponds to the blue line of Fig. 3
   • Output: Numerical matrix containing the full cSMC-PMMH trajectory

Execution:

• Both scripts are independent

Cubic_SDE Script

Pupose

Reproduces the convergence of likelihood result (Fig. 2) on the 1-d cubic SDE.

Dependencies

• mvnfast, MASS, mvtnorm, doParallel

Application Script

Pupose

Reproduces results related to the application on the rat (Fig. 8 and 9)

Customise

• Load the data that was originally in .mat files (Line 1-3)

Dependencies

• mvnfast, MASS, mvtnorm, cSMC