Implementations of the Monte Carlo EM Algorithm

The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the E-step is computed numerically through Monte Carlo simulations. The most flexible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is throu...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	Journal of Computational and Graphical Statistics. - American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America, 1992. - 10(2001), 3, Seite 422-439
1. Verfasser:	Levine, Richard A. (VerfasserIn)
Weitere Verfasser:	Casella, George
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2001
Zugriff auf das übergeordnete Werk:	Journal of Computational and Graphical Statistics
Schlagworte:	Generalized linear mixed models Gibbs sampler Importance sampling Markov chain Monte Carlo Metropolis-Hastings algorithm Regenerative simulation Renewal theory Mathematics Applied sciences Social sciences


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100	1		\|a Levine, Richard A. \|e verfasserin \|4 aut
245	1	0	\|a Implementations of the Monte Carlo EM Algorithm
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520			\|a The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the E-step is computed numerically through Monte Carlo simulations. The most flexible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is through Markov chain Monte Carlo (MCMC) routines such as the Gibbs and Metropolis-Hastings samplers. Although MCMC estimation presents a tractable solution to problems where the E-step is not available in closed form, two issues arise when implementing this MCEM routine: (1) how do we minimize the computational cost in obtaining an MCMC sample? and (2) how do we choose the Monte Carlo sample size? We address the first question through an application of importance sampling whereby samples drawn during previous EM iterations are recycled rather than running an MCMC sampler each MCEM iteration. The second question is addressed through an application of regenerative simulation. We obtain approximate independent and identical samples by subsampling the generated MCMC sample during different renewal periods. Standard central limit theorems may thus be used to gauge Monte Carlo error. In particular, we apply an automated rule for increasing the Monte Carlo sample size when the Monte Carlo error overwhelms the EM estimate at any given iteration. We illustrate our MCEM algorithm through analyses of two datasets fit by generalized linear mixed models. As a part of these applications, we demonstrate the improvement in computational cost and efficiency of our routine over alternative MCEM strategies.
540			\|a Copyright 2001 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
650		4	\|a Generalized linear mixed models
650		4	\|a Gibbs sampler
650		4	\|a Importance sampling
650		4	\|a Markov chain Monte Carlo
650		4	\|a Metropolis-Hastings algorithm
650		4	\|a Regenerative simulation
650		4	\|a Renewal theory
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes \|x Markov chains
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Measures of variability \|x Sample size
650		4	\|a Mathematics \|x Applied mathematics \|x Analytics \|x Analytical estimating \|x Maximum likelihood estimation
650		4	\|a Applied sciences \|x Electronics \|x Electronic equipment \|x Electronic control \|x Burn in
650		4	\|a Social sciences \|x Human geography \|x Political geography \|x Metropolitan areas
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Error rates
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Statistical theories \|x Central limit theorem
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical results \|x Statistical properties \|x Estimate reliability \|x Confidence interval
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Gaussian distributions
655		4	\|a research-article
700	1		\|a Casella, George \|e verfasserin \|4 aut
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773	1	8	\|g volume:10 \|g year:2001 \|g number:3 \|g pages:422-439
856	4	0	\|u https://www.jstor.org/stable/1391097 \|3 Volltext
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