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Activity Number:
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303
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Statistical Computing*
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| Abstract - #301001 |
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Title:
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Monte Carlo Standard Errors for Markov Chain Monte Carlo EM
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Author(s):
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Galin Jones*+
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Affiliation(s):
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University of Minnesota
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Address:
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347 Ford Hall 224 Church St S.E., Minneapolis, Minnesota, 55455,
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Keywords:
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Markov chain ; Monte Carlo ; EM algorithm ; regenerative simulation ; asymptotic standard errors ; central limit theorem
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Abstract:
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The Monte Carlo EM (MCEM) algorithm is a popular method for maximizing intractable likelihoods. A key ingredient of successful implementation of MCEM is controlling the Monte Carlo sample size at each iteration. Here the focus will be on two methods of using regenerative simulation to assess the relevant Monte Carlo error, when the sampling mechanism in each E-step is Markov chain Monte Carlo (MCMC). The first method is to assess the error in the Q-function so that we can be assured that the ascent property enjoyed by deterministic EM also holds (with high probability) for MCEM. The second method is an extension of Booth and Hobert's (1999) method, which assesses the Monte Carlo error of the parameter estimates at each iteration. Conditions on the underlying MCMC algorithm are derived that guarantee valid standard errors are obtained in both cases.
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