Parallel mcmc

[janfb]

Not sure why we did not do this before, but it seems rather straight forward to parallelize slice_np:

• for the serial version we just use one worker per chain
• for the vectrorized version we give a batch of chains to the workers

Similarly, we can parallize the initialization with SIR which can take quite long with a large numbers of chains and a slow potential function.

This PR adds the num_workers argument to MCMCPosterior and adds a function that performs slice_np parallelized over workers.

We have another refactor of the slice samplers waiting in #607 but we can integrate that later I find.

Still todo:

• add documentation for new functions
• fix pbars

[jan-matthis]

Great! I've left a few comments after a quick first pass over it.

As for "why we did not do this before": Last time I was concerned with the efficiency of the slice sampler implementation was for the benchmark in which all runs were limited to a single core. Vectorizing it improved speed up to 36-fold which was more than enough. Having said that, the ability to additionally parallelize init and sampling across cores is a great addition!

[codecov-commenter]

Codecov Report

Merging #648 (f9ecde9) into main (78cc11e) will increase coverage by 0.22%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #648      +/-   ##
==========================================
+ Coverage   74.81%   75.03%   +0.22%     
==========================================
  Files          75       74       -1     
  Lines        5667     5673       +6     
==========================================
+ Hits         4240     4257      +17     
+ Misses       1427     1416      -11     

Flag	Coverage Δ
unittests	75.03% <100.00%> (+0.22%)	⬆️

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

Impacted Files	Coverage Δ
sbi/inference/posteriors/mcmc_posterior.py	70.99% <100.00%> (-2.25%)	⬇️
sbi/samplers/__init__.py	100.00% <100.00%> (ø)
sbi/samplers/mcmc/__init__.py	100.00% <100.00%> (ø)
sbi/samplers/mcmc/slice_numpy.py	95.73% <100.00%> (+17.01%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 78cc11e...f9ecde9. Read the comment docs.

[michaeldeistler]

Thanks for creating this! I'm fine with merging this once JML's comments are addressed

[jan-matthis]

Cheers!