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Monday, February 29, 2001 4:30 PM in REC 113 Mr. Galin Jones University of FLorida will speak on Honest Exploration of Intractable Probability Distributions Via Markov Chain Monte Carlo Abstract Two important questions that should be answered whenever a 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.
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