Roll our own summary

[rlouf]

Numpyro has a nice numpyro.diagnostics.print_summary function to print diagnostics for the chains. However:

1. It feels wasteful to import numpyro just for this functionality;
2. Blackjax implements the same diagnostics
3. Blackjax may have more diagnostics in the future, see Add (Kernelized) Stein discrepancy diagnostic blackjax#384 and Add nested Rhat diagnostic blackjax#278

I think we should thus implement our own function that prints a summary with different diagnostics; this will certainly be useful when comparing the results from different algorithms.

[junpenglao]

I think we should use https://python.arviz.org/en/stable/ for this.

Note that we have rhat and ess currently for the reason that we might want to explore using these for tuning. So I will apply the same logic when consider adding new diagnostics)

[albcab]

Agree with @junpenglao that we don't need to be a diagnostics library, just use arviz.

But maybe we can use some of these diagnostics on testing?

[rlouf]

I agree with both of you, closing for now.