RandMaxVar update and batch acquisitions

[uremes]

Summary:

The randmaxvar acquisitions are sampled from the maxvar acquisition function with an MCMC sampler. Two updates are proposed here:

1. add option to use prior distribution in sampler initialisation

The acquisition method needs to initialise the MCMC sampler with a point that has maxvar acquisition score (approximate posterior variance) above zero. The current version samples candidate points from a uniform distribution within BOLFI bounds. The updated version includes an option to sample from the prior distribution.

2. batch acquisitions

The current implementation runs one MCMC chain and returns the batch_size last samples. This works when batch_size=1 but does not provide a representative sample from the maxvar acquisition function otherwise. The version proposed in this update returns the last mcmc sample when batch_size=1 and a random sample from the MCMC chain otherwise.

For illustration, here are batches acquired by running BOLFI on the MA2 example with log-discrepancies using batch_size=10 and the current randmaxvar implementation with sampler=’metropolis’ and n_samples=2000. The batches tend to include 2-4 unique parameter values:

These are batches acquired by running the same example using the updated implementation with the same parameters as above and warmup=500. Most batches now include 10 unique parameter values:

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• You have included or updated all the relevant documentation, including docstrings
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[uremes]

addressed the feedback that users may not want the prior to be used in sampler initialisation. default option is now to use the uniform distribution, and the user needs to set init_from_prior=True to sample from the prior instead.