Importance sampler

[michaeldeistler]

This implements an ImportanceSamplingPosterior.

This posterior behaves as follows:

• log_prob(): estimates the normalization constant of the potential_fn with importance sampling and then returns the potential_fn(theta) - log(norm_constant).
• sample(): Depending on method, it either returns samples from the proposal and their corresponding importance weights or it samples with SIR (default)

Also, I realized that the "sir" init in MCMC does not actually perform SIR. SIR resamples with weights p(theta|x) / q(theta), but our weights were simply p(theta|x). I renamed this init to resample. resample is also the default. Setting init_strategy='sir' will perform "actual" SIR.

[codecov-commenter]

Codecov Report

Merging #692 (ddc43a0) into main (3405f8b) will decrease coverage by 0.82%.
The diff coverage is 54.21%.

❗ Current head ddc43a0 differs from pull request most recent head bcc6a09. Consider uploading reports for the commit bcc6a09 to get more accurate results

@@            Coverage Diff             @@
##             main     #692      +/-   ##
==========================================
- Coverage   77.30%   76.47%   -0.83%     
==========================================
  Files          76       78       +2     
  Lines        5869     5930      +61     
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- Hits         4537     4535       -2     
- Misses       1332     1395      +63     

Flag	Coverage Δ
unittests	76.47% <54.21%> (-0.83%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
sbi/inference/posteriors/rejection_posterior.py	82.05% <ø> (-0.45%)	⬇️
sbi/samplers/vi/__init__.py	100.00% <ø> (ø)
sbi/samplers/vi/vi_utils.py	75.97% <ø> (-0.71%)	⬇️
sbi/samplers/importance/sir.py	23.07% <23.07%> (ø)
sbi/inference/posteriors/importance_posterior.py	29.03% <29.03%> (ø)
sbi/inference/posteriors/mcmc_posterior.py	68.79% <60.00%> (-0.78%)	⬇️
sbi/samplers/mcmc/init_strategy.py	83.78% <60.00%> (-4.10%)	⬇️
sbi/samplers/importance/importance_sampling.py	86.20% <86.20%> (ø)
sbi/inference/__init__.py	100.00% <100.00%> (ø)
sbi/inference/posteriors/__init__.py	100.00% <100.00%> (ø)
... and 3 more

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[janfb]

Great PR!
see comments below.

[janfb]

Great to have the additional sampling methods as Posteriors as well!
Once this one and the arViz PR #542 (I am on it) are both merged we should set up a benchmark to see how they compare and to see which hyperparameters to use!