Compute Metropolis average accept probability with logsumexp

[jessegrabowski]

In the Metropolis step stats that we report on the progressbar, we have a probability of acceptance. This is currently computed in a very direct way, just np.mean(np.exp(log_accept_prob)). We can do better with np.exp(logsumexp(log_accept_prob) - log(len(log_accept_prob))).

In really gnarly models, I've encountered overflows in this step. This might also be because there's a max(delta_logp, 1) missing from the acceptance probabilities. But even if we add that, the computation method in this PR is more numerically stable and accurate.

---

📚 Documentation preview 📚: https://pymc--7783.org.readthedocs.build/en/7783/

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.84%. Comparing base (bd28ee9) to head (0827196).
Report is 11 commits behind head on main.

Additional details and impacted files

@@ Coverage Diff @@ ## main #7783 +/- ## ========================================== + Coverage 92.83% 92.84% +0.01%  ========================================== Files 107 107 Lines 18354 18381 +27 ========================================== + Hits 17039 17066 +27  Misses 1315 1315 

Files with missing lines	Coverage Δ
pymc/step_methods/metropolis.py	93.24% <100.00%> (+0.01%)	⬆️

... and 2 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[jessegrabowski]

@ricardoV94 any thoughts about just clipping the acceptance probability to be in 0,1 ?

[ricardoV94]

@ricardoV94 any thoughts about just clipping the acceptance probability to be in 0,1 ?

Is that why you were getting nans after the exp? Shouldn't hurt, as long as it's all cheap stuff

[jessegrabowski]

Yes I assume it was overflowing. In the progress bar I was seeing large values for acceptance

[ricardoV94]

Yes I assume it was overflowing. In the progress bar I was seeing large values for acceptance

Then feel free to clip the exp from above or the log to be at most 0 for the returned stat