Adapting the Metropolis Algorithm

Tuesday, March 23, 2021 - 1:25pm - 2:25pm
Jeffrey Rosenthal (University of Toronto)

The Metropolis Algorithm is an extremely useful and popular method of approximately sampling from complicated probability distributions. "Adaptive" versions automatically modify the algorithm while it runs, to improve its performance on the fly, but at the risk of destroying the Markov chain properties necessary for the algorithm to be valid.  In this talk, we will illustrate the Metropolis algorithm using a very simple JavaScript example (  We will then discuss adaptive MCMC, and present examples and theorems concerning its ergodicity and efficiency.

Jeffrey S. Rosenthal is a professor of Statistics at the University of Toronto, specializing in Markov chain Monte Carlo (MCMC) algorithms. He received his BSc from the University of Toronto at age 20, and his PhD in Mathematics from Harvard University at age 24. He was awarded the 2006 CRM-SSC Prize, the 2007 COPSS Presidents' Award, the 2013 SSC Gold Medal, and fellowship of the Institute of athematical Statistics and of the Royal Society of Canada. He has published well over one hundred research papers, and five books (including the Canadian bestseller Struck by Lightning: The Curious World of Probabilities). His web site is, and on Twitter he is @ProbabilityProf.