News & Events

Subscribe to email list

Please select the email list(s) to which you wish to subscribe.

User menu

You are here

Improving multiple-try Metropolis with local balancing

Tuesday, June 14, 2022 - 11:00 to 12:00
Philippe Gagnon, Assistant Professor of Actuarial Science, Department of Mathematics and Statistics, Université de Montréal
Statistics Seminar
Zoom / ESB 4192

To join via Zoom: Please request Zoom connection details from headsec [at]

Title: Improving multiple-try Metropolis with local balancing

Abstract: Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo algorithm which is amenable to parallel computing and thus has great potential. At each iteration, it samples several candidates for the next state of the Markov chain and randomly selects one of them based on a weight function. By leveraging a connection with the work of Zanella (2020), we show that the preferred choice of weight function in the literature, which is proportional to the target density, induces pathological behaviours in high dimensions. Those pathological behaviours are demonstrated through numerical experiments and theoretical results. We propose different weight functions for which those pathological behaviours do not arise. Also, we provide a scaling-limit analysis that allows to characterize the scalability with respect to the dimension of MTM when using the preferred weight function and when using a proposed weight function. In each case, MTM is seen as an approximation to a limiting sampling scheme which is approached under conditions on the rate at which the number of candidates increases with the dimension.