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.