Revised Rhatv5 and ESS paper (me, @andrewgelman, @anon75146577, @Bob_Carpenter, @paul.buerkner) now in https://arxiv.org/abs/1903.08008.
We’ve tried to improve clarity and added more details, references, and relations to other algorithms. Only minor changes in the algorithm code.
Especially the sections describing how to estimate effective sample size (ESS) from multiple chains correctly (Section 3.2) and how to estimate Monte Carlo standard error for quantiles (Section 4.4) have been much improved.
These methods are implemented at least in R in RStan summary() and posterior package (used by CmdStanR, too), and in Python in ArviZ package. The description in the paper is also the best description for Rhatv4 and n_eff still shown by summary command in CmdStan.
New Rhatv5 and ESS have been previously
discussed, for example, in thread New R-hat and ESS.