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Revisiting the Gelman-Rubin Diagnostic

PRIISM Seminar guest speaker, Professor Christina Knudson
(1 hour)

PRIISM Seminar by Christina Knudson

Wednesday, February 24, 2021

11:00 am - 12:00 pm ET

Zoom (this event will be recorded)


Revisiting the Gelman-Rubin Diagnostic

A better way to terminate your MCMC sampler!

Interested in learning about Markov chain Monte Carlo (MCMC) techniques? Join us for an in-depth look into new connections between the Gelman-Rubin statistic and Monte Carlo variance estimators presented by Dr. Christina Knudson, an expert in generalized linear mixed models and MCMC methods.


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.


Dr. Knudson is an assistant professor of statistics at the University of St. Thomas. She earned her Ph.D. from the School of Statistics at the University of Minnesota in 2016. Dr. Knudson's research focuses mostly on statistical methodology, with two of her main topics being generalized linear mixed models and MCMC sample analysis. She maintains the R packages glmm and stableGR. 

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