# Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC

arXiv: https://arxiv.org/abs/1903.08008 · HTML: https://mlsanity.com/paper/1903.08008/

## Key facts

- Cited by 93 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

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## Abstract (arXiv)

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 widehatR of Gelman and Rubin (1992) has serious flaws. Traditional widehatR 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.