An Improved Collapsed Gibbs Sampler for Dirichlet Process Mixing Models

Abstract

We propose a nonparametric Bayesian formultation for the frequency counts in a two-way contingency table. The formulation based on the mixtures of Dirichlet processes provides a natural framework for a cluster analysis in the contingency table, because it specifies probabilities respectively to clusters of the subjects sharing the same classification probabilities. To improve the current collapsed Gibbs sampler for this kind of Dirichlet processes mixing problems, we will develop a further improved collapsed Gibbs sampler. The new one is obtained by sampling the classification probabilities for each subject marginally, integrating out the other subjects' classification probabilities. The performance of the new Gibbs sampler will be compared to the existing one, especially for large contingency tables and testing for homogeneity as described by Quintana (1998). Similarly, we can apply the method to a DNA sequences data (for example, in Liu, 1994) to determine whether or not the residue frequency is independent of the position in a protein binding site.