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November 2021 Revisiting the Gelman–Rubin Diagnostic
Dootika Vats, Christina Knudson
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Statist. Sci. 36(4): 518-529 (November 2021). DOI: 10.1214/20-STS812

Abstract

Gelman and Rubin’s (Statist. Sci. 7 (1992) 457–472) convergence diagnostic is one of the most popular methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the seminal paper, researchers have developed sophisticated methods for estimating variance of Monte Carlo averages. We show that these estimators find immediate use in the Gelman–Rubin statistic, a connection not previously established in the literature. We incorporate these estimators to upgrade both the univariate and multivariate Gelman–Rubin statistics, leading to improved stability in MCMC termination time. An immediate advantage is that our new Gelman–Rubin statistic can be calculated for a single chain. In addition, we establish a one-to-one relationship between the Gelman–Rubin statistic and effective sample size. Leveraging this relationship, we develop a principled termination criterion for the Gelman–Rubin statistic. Finally, we demonstrate the utility of our improved diagnostic via examples.

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Dootika Vats. Christina Knudson. "Revisiting the Gelman–Rubin Diagnostic." Statist. Sci. 36 (4) 518 - 529, November 2021. https://doi.org/10.1214/20-STS812

Information

Published: November 2021
First available in Project Euclid: 11 October 2021

Digital Object Identifier: 10.1214/20-STS812

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.36 • No. 4 • November 2021
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