Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)

By Aki Vehtari, Andrew Gelman, Daniel P. Simpson, Bob Carpenter, Paul-Christian Burkner. Bayesian Analysis, 2019

1,440 citations recorded by the source corpus.

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 $\widehat{R}$ of Gelman and Rubin (1992) has serious flaws. Traditional $\widehat{R}$ 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.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5f0b75a41dc87ba5877e2cd8f84e8d7e70883711

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In Management Science and Operations Research

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Citations in the corpus

dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences (2019, background): “While optimization techniques can speed up this process, assessing this convergence can be challenging and time-consuming (Gelman & Rubin 1992; Vehtari et al. 2019).”
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors (2020, methodology): “To monitor within-chain mixing, we use split-(cid:98) R (Vehtari et al., 2021).”
An approximate sampler for energy-based models with divergence diagnostics (2022, background): “For instance, popular convergence assessments such as effective sample size (ESS) (Gamerman and Lopes, 2006) or R̂ (Gelman and Rubin, 1992; Vehtari et al., 2021) require Euclidean structure for computing variances and correlations of real-valued variables (or vectors in multivariate generalizations;”
Pathfinder: Parallel quasi-Newton variational inference (2021, neutral): “A less strict criterion only requires adequate mixing of the chains, which may be measured through within- and between-chain variances (Gelman and Rubin, 1992; Vehtari et al., 2021).”