Abstract #300520

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JSM 2002 Abstract #300520
Activity Number: 140
Type: Topic Contributed
Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing*
Abstract - #300520
Title: An Automated (Markov Chain) Monte Carlo EM Algorithm
Author(s): Richard Levine*+
Affiliation(s): University of California, Davis
Address: One Shields Avenue, Davis, California, 95616, USA
Keywords: Gibbs sampler ; Metropolis-Hastings algorithm ; importance sampling ; regenerative simulation ; renewal theory ; generalized linear mixed models
Abstract:

We present an automated Monte Carlo EM (MCEM) algorithm, which efficiently assesses Monte Carlo error in the presence of dependent Monte Carlo--particularly Markov chain Monte Carlo and E-step samples--and chooses an appropriate Monte Carlo sample size to minimize this Monte Carlo error with respect to progressive EM step estimates. Monte Carlo error is gauged through an application of the central-limit theorem during renewal periods of the MCMC sampler used in the E-step. The resulting normal approximation allows us to construct a rigorous and adaptive rule for updating the Monte Carlo sample size each iteration of the MCEM algorithm. We illustrate our automated routine and compare the performance with competing MCEM algorithms in an analysis of a data set fit by a generalized linear mixed model.

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Revised March 2002