On the Use of Posterior Probabilistic Clustering

Abstract

Bayesian approach to mixture models makes use of Gibbs sampler, the most common of Markov Chain Monte Carlo (MCMC), for estimation of posterior density and subsequent classification of objects into components of mixture, especially for conjugate priors. In practice conjugacy may not exist and when it does, the time required calculating the posterior density will be far too high for the Bayesian approach to be applied in practice (McLachlan and Peel, 2000). Therefore, we developed a clustering procedure that is a result of using non-conjugate prior distribution of product multinomial to obtain posterior distribution that is hypergeometric, for cross-classifying categorical data. The performance of the scheme was examined through a simulation study of observed tables of counts compared with expected generated by assuming product multinomial to obtain posterior distribution under variety of parameter distributions and loadings. We observed that the approach performed well when the component proportions are properly distinguishable. The approach was illustrated using real life data from social science.