Spring 2009 Thursday, April 30   Speaker: George Casella, Ph.D. Department of Statistics University of Florida Title: "Estimation in Dirichlet Random Effects Models " 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 distribution, 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 concentration parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach.  Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.  Much of this work was motivated by applications in the social sciences, and we apply out methods to data from the Scottish Parliamentary Elections of 1997.

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