Rank-normalization, folding, and localization: An improved R for assessing convergence of MCMC
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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 and we propose an alternative that fixes them. 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 concrete recommendations for how these methods should be used in practice.
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