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Cited by 1,810Markov Chains and Monte Carlo MethodsStatistical Methods and Bayesian InferenceData Analysis with R

The DOI matches its Crossref record; 45 of the 47 references it cites were found in a registry or an index, and 2 are not checked yet.

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

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Vehtari, Aki, Gelman, Andrew, Simpson, Daniel, Carpenter, Bob, Bürkner, Paul-Christian·2021·Bayesian Analysis
DOI 10.1214/20-ba1221
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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 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.

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  1. Blom, G. (1958). Statistical Estimates and Transformed Beta-Variables. Wiley; New York.
  2. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis, third edition. CRC Press. · DOI · Paper page
  3. Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., and Bürkner, P.-C. (2020). “Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC. Supplementary Material.” Bayesian Analysis. · DOI

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Metadata

Authors
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C.
Affiliations
  • Aalto University (FI)
  • Columbia University (US)
  • University of Toronto (CA)
  • Flatiron Institute (US)
ORCID
Venue
Bayesian Analysis
Publisher
Institute of Mathematical Statistics
Published
2021-06-01
Volume
16
Issue
2
Pages
667-718
ISSN
  • 1931-6690 (ISSN-L)
  • 1936-0975
DOI
10.1214/20-ba1221
OpenAlex
W2920804790
Cited by
1,810
References
32
Citations by year
2026: 499 · 2025: 424 · 2024: 328 · 2023: 263 · 2022: 153 · 2021: 93
FWCI
96.56
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Bayesian Analysis (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • HAL (submittedVersion, other-oa)
  • Aaltodoc (Aalto University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
Keywords
convergence diagnostics, Markov chain Monte Carlo, heavy-tailed distributions, Monte Carlo error estimation, trace plots

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