Revisiting the Gelman–Rubin Diagnostic

By Dootika Vats, Christina Knudson. Statistical Science, 2018

182 citations recorded by the source corpus.

Gelman and Rubin's (1992) 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e1dd381b0cd809945db50d53e17b9a0079c50a21

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Citations in the corpus

Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion) (2019, background): “A small value of R̂ is not enough to ensure that an MCMC sample is useful in practice (Vats and Knudson, 2018).”
Learning Energy-based Model with Flow-based Backbone by Neural Transport MCMC (2020, unknown): “Both estimators are consistent for σ 2 as n → ∞ [55].”