Estimating Mixture of Dirichlet Process Models

Current Gibbs sampling schemes in mixture of Dirichlet process (MDP) models are restricted to using \conjugate" base measures which allow analytic evaluation of the transition probabilities when resampling con gurations, or alternatively need to rely on approximate numeric evaluations of some transition probabilities. Implementation of Gibbs sampling in more general MDP models is an open and important problem since most applications call for the use of non-conjugate base measures. In this paper we propose a conceptual framework for computational strategies. This framework provides a perspective on current methods, facilitates comparisons between them, and leads to several new methods that expand the scope of MDP models to non-conjugate situations. We discuss one in detail. The basic strategy is based on expanding the parameter vector, and is applicable for MDP models with arbitrary base measure and likelihood. Strategies are also presented for the important class of normal-normal MDP models and for problems with xed or few hyperparameters. The proposed algorithms are easily implemented and illustrated with an application.