Test HMC and MALA against each other

[WardBrian]

This adds a test which uses the statement "MALA is equivalent to HMC with 1 step" to test HMC and MALA against one another.

It's a neat test, but I also think this is cool for serving the pedagogical goals of the package as well. It's cool to see that they are literally equivalent up to some scaling on the step size.

This also fixes an issue @jsoules noticed with the BetaBinom test model returning a gradient which was off by a constant multiple from the real gradient.

[codecov-commenter]

Codecov Report

Merging #18 (08c6545) into main (22a3e9f) will increase coverage by 0.03%. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main      #18      +/-   ##
==========================================
+ Coverage   95.68%   95.71%   +0.03%     
==========================================
  Files           9        9              
  Lines         255      257       +2     
==========================================
+ Hits          244      246       +2     
  Misses         11       11              

Impacted Files	Coverage Δ
bayes_kit/__init__.py	100.00% <100.00%> (ø)

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[jsoules]

Looks good to me if we can fix whatever's going on with the HMC beta binomial test.

[WardBrian]

Fixing the gradient calculation seems to have made the mala test less stable as well. I’m sure we can find another sort of island of stability by tuning step sizes, I’ll try some more tomorrow (annoyingly I seem to have quite good luck on my local machine, so even the current step size refuses to fail!)

[WardBrian]

I seem to have found some slightly better settings without it taking much longer than it did before

[WardBrian]

Merging now, will follow on with a PR to unconstrain the binomial model