文章基本信息

标题：Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)
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作者：Aki Vehtari ; Andrew Gelman ; Daniel Simpson 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2021
卷号：16
期号：2
页码：667-718
DOI：10.1214/20-BA1221
语种：English
出版社：International Society for Bayesian Analysis
摘要：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 Rˆ of Gelman and Rubin (1992) has serious flaws. Traditional Rˆ 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.