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.
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For the reference, earlier multi-chain Rhats are v1 Gelman & Rubin, 1992 v2 Brooks & Gelman, 1998 v3 BDA2, Gelman et al, 2003 v4 BDA3, Gelman et al, 2013 (the differences are mentioned in v5 paper)
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There are some other papers proposing single-chain Rhat, but for us the Rhat method is specifically useful for multi-chain as diagnostic *and* as a part of correctly estimating multi-chain ESS. For a single chain, ESS and MCSE are sufficient (if you can trust that single chain).
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Do you have a typo in titles of second row histograms in figure 2 or I’m not understanding something? Shouldn’t it be infinite variance?
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If the mean is infinite then the variance is also infinite. Since the example uses Cauchy, both mean and variance are infinite.
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