ESTIMATING MIXTURE OF DIRICHLET PROCESS MODELS

Current Gibbs sampling schemes in mixture of Dirichlet process (MDP) m odels are restricted to using ''conjugate'' base measures that allow a nalytic evaluation of the transition probabilities when resampling con figurations, or alternatively need to rely on approximate numeric eval uations of some transition probabilities. Implementation of Gibbs samp ling in more general MDP models is an open and important problem becau se most applications call for the use of nonconjugate base measures, I n this article we propose a conceptual framework for computational str ategies. This framework provides a perspective on current methods, fac ilitates comparisons between them, and leads to several new methods th at expand the scope of MDP models to nonconjugate situations. We discu ss one in detail. The basic strategy is based on expanding the paramet er vector, and is applicable for MDP models with arbitrary base measur e and likelihood. Strategies are also presented for the important clas s of normal-normal MDP models and for problems with fixed or few hyper parameters, The proposed algorithms are easily implemented and illustr ated with an application.