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Abstract: We develop a new Gibbs sampler for a linear mixed model with a Dirichletprocess random effect term, which is easily extended to a generalized linearmixed model with a probit link function. Our Gibbs sampler exploits theproperties of the multinomial and Dirichlet distributions, and is shown to bean improvement, in terms of operator norm and efficiency, over other commonlyused MCMC algorithms. We also investigate methods for the estimation of theprecision parameter of the Dirichlet process, finding that maximum likelihoodmay not be desirable, but a posterior mode is a reasonable approach. Examplesare given to show how these models perform on real data. Our results complementboth the theoretical basis of the Dirichlet process nonparametric prior and thecomputational work that has been done to date.



Author: Minjung Kyung, Jeff Gill, George Casella

Source: https://arxiv.org/



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