Estimation in Dirichlet random effects models

TL;DR

This paper introduces an improved Gibbs sampler for Dirichlet process mixed models, enhancing computational efficiency and providing practical methods for estimating the process's precision parameter, with applications to real data.

Contribution

The paper presents a novel Gibbs sampling algorithm for Dirichlet random effects models and explores estimation methods for the Dirichlet process's precision parameter.

Findings

The new Gibbs sampler outperforms existing algorithms in efficiency.

Posterior mode estimation is preferable over maximum likelihood for the precision parameter.

Models demonstrate effective performance on real datasets.

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.