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Revisiting Gelman-Rubin with Global Centering

Photo of Dootika Vats
Monday, May 09, 2022
12:00 pm - 1:00 pm
Dootika Vats is an Assistant Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur, India.

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 further identify that variance estimation of Monte Carlo can be vastly improved for parallel chains by using global centering. This leads to more accurate ACF plots and an improved estimator of the Gelman-Rubin statistic. Finally, we establish a one-to-one relationship between the Gelman-Rubin statistic and effective sample size, leveraging which, we develop a principled termination criterion for the Gelman-Rubin statistic.

Bio: Dootika Vats is an Assistant Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur, India. Before moving to Kanpur, she was an NSF Postdocotoral fellow at the University of Warwick and obtained her PhD from the School of Statistics at the University of Minnesota, Twin-Cities. She works in the general area of Bayesian computation and specifically focuses on Markov chain Monte Carlo algorithms.

Contact: Karen Whitesell