Open Access
April 2010 Estimation in Dirichlet random effects models
Minjung Kyung, Jeff Gill, George Casella
Ann. Statist. 38(2): 979-1009 (April 2010). DOI: 10.1214/09-AOS731


We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.


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Minjung Kyung. Jeff Gill. George Casella. "Estimation in Dirichlet random effects models." Ann. Statist. 38 (2) 979 - 1009, April 2010.


Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62034
MathSciNet: MR2604702
Digital Object Identifier: 10.1214/09-AOS731

Primary: 62F99
Secondary: 62G99 , 62P25

Keywords: Bayes estimation , generalized linear mixed models , Gibbs sampling , hierarchical models , linear mixed models

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 2 • April 2010
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