fix: ImproperEmpirical is inefficient

[gmoss13]

Addresses #1635

As mentioned in #1635, ImproperEmpirical currently saves all the prior samples. However, these samples are never actually used, and ImproperEmpirical itself is only used for single round, posterior-estimation methods (so NPE, NPSE, MNPE, etc.), and even when it is used, we turn off mcmc_transform. We currently warn the user if the number of samples is big, that the memory usage will be large.

This PR makes some changes to ImproperEmpirical:

• Instead of saving all the samples, it simply computes the mean and standard deviation of the samples
• It allows mcmc_transform to z-score the parameters even when the prior is ImproperEmpirical (this was turned off before)
• It raises a warning if sample() or log_prob() is called for ImproperEmpirical. The first we have to turn off if we don't want to save the samples. In principle, we can keep the current behaviour for log_prob of returning zeros for any value, but this is a bit weird for me - an empirical prior is unlikely to actually be uniform (improper), and if we need to call log_prob(), we would want the values to reflect what the log prob actually is (so either a proper prior, or to use the pyro.Empirical if we don't know what the prior is, which would be a mixture of delta distributions). Raising this warning did not create any test failures, because we never call log_prob() when using ImproperEmpirical

[codecov]

Codecov Report

❌ Patch coverage is 79.41176% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.66%. Comparing base (06f13a8) to head (cce6553).
⚠️ Report is 2 commits behind head on main.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
sbi/utils/sbiutils.py	79.41%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1700      +/-   ##
==========================================
- Coverage   88.48%   84.66%   -3.82%     
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  Files         137      137              
  Lines       11470    11484      +14     
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- Hits        10149     9723     -426     
- Misses       1321     1761     +440     

Flag	Coverage Δ
unittests	84.66% <79.41%> (-3.82%)	⬇️

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

Files with missing lines	Coverage Δ
.../inference/potentials/posterior_based_potential.py	84.00% <ø> (+4.75%)	⬆️
sbi/inference/trainers/npe/npe_base.py	93.54% <ø> (+0.63%)	⬆️
sbi/utils/sbiutils.py	79.68% <79.41%> (-8.12%)	⬇️

... and 26 files with indirect coverage changes

[janfb]

Looks good! Thanks for looking into this @gmoss13 !