Spring 2001 Seminar Series - February 20, 2001
University of Minnesota
School of Statistics
College of Liberal Arts

A Markov Chain Monte Carlo Algorithm for Approximating Exact Conditional Probabilities

Brian S. Caffo
University of Florida
(Statistics Search Candidate)

Tuesday, February 20, 2001
4:00 PM, 211 Vincent Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300 Ford Hall

Abstract

Conditional inference eliminates nuisance parameters by conditioning on their sufficient statistics. For contingency tables conditional inference entails enumerating all tables with the same sufficient statistics as the observed data. For moderately sized tables and/or complex models the computing time to enumerate these tables is often prohibitive. Monte Carlo approximations offer a viable alternative provided it is possible to obtain samples from the correct conditional distribution. This talk presents an MCMC extension of the importance sampling algorithm of Booth and Butler 1999 by utilizing their rounded normal candidate to update randomly chosen cells while leaving the remainder of the table fixed. This local approximation can greatly increase the efficiency of the rounded normal candidate. By choosing the number of cells to be updated at random, a balance is struck between dependency in the Markov chain and accuracy of the candidate.