Fall 2002 Seminar Series - October 24, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Coupling Constructions for Markov Chains
Jeffrey S. Rosenthal
University of Toronto
Thursday, October 24, 2002
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
We consider the use of coupling techniques to obtain quantitative
bounds on the convergence to stationarity of Markov chains -- a problem
of great importance for MCMC algorithms. We first review coupling constructions
using minorisation and drift conditions, and apply them to various Gibbs
sampler algorithms. We then present a new coupling construction, one-shot
coupling, which waits until the last possible moment before attempting to
couple. We apply this construction to a Markov chain on the means of Dirichlet
processes.
Some of this is joint work with G.O. Roberts.