Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC

Aki Vehtari*, Andrew Gelman, Daniel Simpson, Bob Carpenter, Paul-Christian Burkner

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

37 Citations (Scopus)
51 Downloads (Pure)

Abstract

Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic R of Gelman and Rubin (1992) has serious flaws. Traditional R will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.
Original languageEnglish
Pages (from-to)667-718
Number of pages52
JournalBayesian Analysis
Volume16
Issue number2
DOIs
Publication statusPublished - Jun 2021
MoE publication typeA1 Journal article-refereed

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