Spring 2001 Seminar Series - February 13, 2001
University of Minnesota
School of Statistics
College of Liberal Arts
Honest Exploration of Intractable Probability Distributions via Markov
Chain Monte Carlo
Galin Jones
University of Florida
(Statistics Search Candidate)
Tuesday, February 13, 2001
4:00 PM,
229
Lind Hall
Minneapolis, East Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Two important questions that should be answered whenever Markov chain Monte Carlo
(MCMC) algorithm is employed are (Q1) What is an appropriate burn-in? and (Q2)
How long should the sampling continue after burn-in? Developing rigorous
answers to these questions presently requires a detailed study of the
convergence properties of the underlying Markov chain. Consequently, in most
practical applications of MCMC, exact answers to (Q1) and (Q2) are not sought.
The ability to formally address (Q1) and (Q2) comes from establishing a drift
condition and an associated minorization condition, which together imply that
the chain is geometrically ergodic. I explain what drift and minorization are
as well as why these conditions can be used to form rigorous answers to (Q1)
and (Q2). The fundamental technique is illustrated with a toy example. I then
present the results of applying this approach to a realistic hierarchical
random effects model.