Estimation in Dirichlet random effects models

Details Estimation in Dirichlet random effects models Estimation in Dirichlet random effects models

Publishing date

2010-02-25

URL

arxiv.org/abs/1002.4756v1

Journals

Annals of Statistics 2010, Vol. 38, No. 2, 979-1009

Science

Mathematics

Field

Statistics Theory

Additional info

Published in at http://dx.doi.org/10.1214/09-AOS731 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Type

Scientific paper

Digital Object Identifier

10.1214/09-AOS731

Abstract

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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