| DATE: | Thursday, February 8, 2001 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Wolfgang Wefelmeyer |
| TITLE: | Statistics applied to MCMC |
It is often difficult to calculate the expectation of a function analytically or even by numerical integration. In this situation one may sometimes resort to Markov chain Monte Carlo (MCMC) methods. These methods generate a Markov chain with the given distribution as stationary law. Then the expectation may be approximated by the empirical estimator based on realizations from the chain. A typical (probabilistic) question is: How fast does the chain converge to stationarity? In this talk we judge MCMC methods by a statistical criterion: the asymptotic variance of estimators based on realizations from MCMC chains. We consider the following questions. What is the asymptotic variance of empirical estimators for Gibbs samplers? Is it better to use random or deterministic sweep? How much of the information contained in the realizations is exploited by the empirical estimator? If the given distribution is a random field, how can we improve the empirical estimator if the field has certain symmetries, or local interactions of a certain range? The talk is based on joint work with P. E. Greenwood (Arizona State University, Tempe) and I. W. McKeague (Florida State University, Tallahassee).