Functions for calculating the DA estimator

[louisekluge]

Facilities for calculating the the MLDA estimator in the two-level case, as well as associated variances

[louisekluge]

Hi, I am still trying to figure out many things and a few questions with regard to design have come up:

1. Do you generally think that the two functions as I sketched them are suitable?
2. If I want to do the get_DA_samples function in analogy to get_samples, I need to modify sampler.py first, so that it the dict that is returned by tda.sample contains also promoted_coarse? Is that something we want generally in the two level/multilevel case?

[mikkelbue]

@louisekluge

1. I think the best way to do this would be to allow compiling an InferenceData object for the promoted_coarse samples. That way we could easily compute the difference for any quantity, parameters, or qoi or whatever. I would adapt the get_samples function to accept level="promoted_coarse" as an input to condstruct that InferenceData object. Then we can use a function like the one you have sketched DA_estimator(inferencedata_fine, inferencedata_coarse_promoted, attribute) to compute the estimator.
2. Yes you would have to modify sampler.py to return the additional list. I have made some changes to the RemoteChain class that handles the parallelisation which should make this a lot easier for the parallel case. They are on this branch https://github.com/mikkelbue/tinyDA/tree/mikkel-ray_refactor .. Could you test that branch for me? Then I will merge it.

[louisekluge]

Hi, I think this is ok now. I did some tests with the Multilevel Delayed Acceptance notebook setup and it works fine I think.

[mikkelbue]

Looks good. I have a couple of stylistic suggestions. Please can you also run black on the code?

[louisekluge]

I had a thought about burnin: when I subtract the burnin in calculating the multilevel estimator, the burnin subtracted on the coarse level should be burnin*subchain_length, as burnin generally refers to the fine chain. I will adapt this accordingly.

[mikkelbue]

Looks good. Please add some comments that explains what the code does throughout. Thanks!

[mikkelbue]

Why not just compute the mean directly rather than the entire summary and then extract the mean. There should be a faster way of doing this.