ESTIMATION IN DIRICHLET RANDOM EFFECTS MODELS

• 成果类型: Article
• 署名作者: Kyung, Minjung; Gill, Jeff; Casella, George
• 署名单位: State University System of Florida; University of Florida; Washington University (WUSTL)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS731
• 发表日期: 2010
• 页码: 979-1009
• 关键词: bayesian nonparametric-estimation; generalized linear-models; product partition models; inference; distributions; algorithms; mixtures; binary; priors

摘要

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.