On convergence of the EM algorithm and the Gibbs sampler

被引:31
作者
Sahu, SK
Roberts, GO
机构
[1] Univ Wales, Sch Math, Cardiff, S Glam, Wales
[2] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England
关键词
Gaussian distribution; generalized linear mixed models; Markov chain Monte Carlo; parameterization; rate of convergence;
D O I
10.1023/A:1008814227332
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In this article we investigate the relationship between the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM-type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under certain conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models.
引用
收藏
页码:55 / 64
页数:10
相关论文
共 30 条
[1]  
[Anonymous], 1996, Bayesian Statistics
[2]  
Box G, 1992, BAYESIAN INFERENCE S, DOI DOI 10.1002/9781118033197.CH4
[3]   APPROXIMATE INFERENCE IN GENERALIZED LINEAR MIXED MODELS [J].
BRESLOW, NE ;
CLAYTON, DG .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1993, 88 (421) :9-25
[4]  
Crowder M.J., 1978, APPLIED STATISTICS, V27, P34, DOI DOI 10.2307/2346223
[5]   BAYESIAN-INFERENCE FOR GENERALIZED LINEAR AND PROPORTIONAL HAZARDS MODELS VIA GIBBS SAMPLING [J].
DELLAPORTAS, P ;
SMITH, AFM .
APPLIED STATISTICS-JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C, 1993, 42 (03) :443-459
[6]   MAXIMUM LIKELIHOOD FROM INCOMPLETE DATA VIA EM ALGORITHM [J].
DEMPSTER, AP ;
LAIRD, NM ;
RUBIN, DB .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1977, 39 (01) :1-38
[7]  
Gamerman D., 1997, MARKOV CHAIN MONTE C
[8]   EFFICIENT PARAMETRIZATIONS FOR NORMAL LINEAR MIXED MODELS [J].
GELFAND, AE ;
SAHU, SK ;
CARLIN, BP .
BIOMETRIKA, 1995, 82 (03) :479-488
[9]  
GELMAN A, 1997, J ROY STAT SOC B, V59, P554
[10]  
Gilks W. R., 1995, MARKOV CHAIN MONTE C