May 13

Math/Stats Colloquium: Christina Knudson

A talk by Christina Knudson (University of St. Thomas)

4:00 – 5:00 pm / Virtually by Zoom

Speaker: Christina Knudson (University of St. Thomas)

Title: An MCMC Convergence Diagnostic: Are We There Yet?

Abstract: 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 (including a Titanic survival model with Jack and Rose).

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Sponsored by Mathematics and Statistics Events. Contact: Sue Jandro