WIP: Enable (naive) minibatching within MCMC.

[odunbar]

Purpose

Content

• New method to decorrelate a vector of data sample vectors
• New emulator posterior function that still enables us to build the (cumbersome) AdvancedMH.DensityModel object. using by defining x -> f(x, emulator, prior, data) in the factory
• emulator posterior now taks 1/n * sum(log(p(y_i|x))) + log_prior(x)over the data vectory_i in Y. This is a naive formulation, requiring n` evaluations of the emulator for every MCMC step.
• added a unit test where 100 slightly perturbed data samples, and acheive the same target.

Misc

The net result of (Barbenet, Doucet, Holmes 2017) ) is that minibatching within MCMC is a very technically complex problem, and for computational benefit without loss of accuracy requires a nested procedure to approximate the accept-reject mechanicsm, and futher surrogates of the log-likelihood. It may be that simple parallelization or alternative (parallel) sampling methods would be preferred

• The ObservationSeries object contains both data samples and noise covariance. Here it appears that MCMC requires only the data samples, while the emulator uses the noise covariance (for decorrelation), this should be addressed in a future issue to do with data processing but not here

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• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

Attention: Patch coverage is 85.71429% with 2 lines in your changes missing coverage. Please review.

Project coverage is 88.92%. Comparing base (2ad4cc7) to head (af0b191).

Files with missing lines	Patch %	Lines
src/MarkovChainMonteCarlo.jl	85.71%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #349      +/-   ##
==========================================
- Coverage   88.96%   88.92%   -0.05%     
==========================================
  Files           7        7              
  Lines        1359     1363       +4     
==========================================
+ Hits         1209     1212       +3     
- Misses        150      151       +1     

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