Spring 2009 Thursday, January 15   Speaker: Aixin Tan Department of Statistics University of Flordia Title: Practical Central Limit Theorem for Markov chain Monte Carlo Estimators Abstract: Markov chain Monte Carlo (MCMC) algorithms are popular computer-based simulation methods that can be used to estimate intractable integrals. An important question that arises when an MCMC algorithm is used in practice is as follows: How many iterations of the algorithm are required to ensure that the estimates achieve a desired precision? To answer this question, one must establish central limit theorems (CLTs) for the MCMC estimators and then develop consistent estimators for the corresponding asymptotic variances. We do this for a specific MCMC algorithm, called the block Gibbs sampler, that is used to explore the intractable posterior distributions associated with Bayesian one-way random effects models. The two key ingredients of our analysis are (1) a proof that the underlying Markov chain converges at a geometric rate, and (2) the identification of regeneration times in the chain.

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