Cited by 6,045Markov Chains and Monte Carlo MethodsStatistical Methods and Bayesian InferenceSimulation Techniques and Applications

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General Methods for Monitoring Convergence of Iterative Simulations

Brooks, Stephen P., Gelman, Andrew·1998·Journal of Computational and Graphical Statistics

DOI 10.1080/10618600.1998.10474787

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Abstract

We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develop convergence-monitoring summaries that are relevant for the purposes for which the simulations are used. We recommend applying a battery of tests for mixing based on the comparison of inferences from individual sequences and from the mixture of sequences. Finally, we discuss multivariate analogues, for assessing convergence of several parameters simultaneously.

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Crossref · 10.1080/10618600.1998.10474787

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Authors: Brooks, S. P., & Gelman, A.
Affiliations: University of Bristol (GB)
Columbia University (US)
ORCID: Brooks, Stephen P.
Gelman, Andrew
Venue: Journal of Computational and Graphical Statistics
Publisher: Informa UK Limited
Published: 1998-12
Volume: 7
Issue: 4
Pages: 434-455
ISSN: 1061-8600 (ISSN-L)
1537-2715
DOI: 10.1080/10618600.1998.10474787
OpenAlex: W2093223772
Cited by: 6,045
References: 28
Citations by year: 2026: 321 · 2025: 371 · 2024: 394 · 2023: 381 · 2022: 341 · 2021: 445 · 2020: 435 · 2019: 370 · 2018: 329 · 2017: 276 · 2016: 305 · 2015: 300 · 2014: 250 · 2013: 244 · 2012: 249
FWCI: 15.55
Type: journal article
Language: en
Open access: closed
Locations: Journal of Computational and Graphical Statistics (publishedVersion)
Bristol Research (University of Bristol) (submittedVersion)
Funders: National Science Foundation
KU Leuven
Engineering and Physical Sciences Research Council
Topics: Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
Keywords: convergence monitoring, Markov chain Monte Carlo, mixing test, simulation-based inference

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General Methods for Monitoring Convergence of Iterative Simulations

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