Bayesian analysis of finite mixtures of multinomial and negative-multinomial distributions

The Bayesian implementation of finite mixtures of distributions has been an area of considerable interest within the literature. Computational advances on approximation techniques such as Markov chain Monte Carlo (MCMC) methods have been a keystone to Bayesian analysis of mixture models. This paper deals with the Bayesian analysis of finite mixtures of two particular types of multidimensional distributions: the multinomial and the negative-multinomial ones. A unified framework addressing the main topics in a Bayesian analysis is developed for the case with a fixed number of component distributions. In particular, theoretical results and algorithms to solve the label-switching problem are provided. An illustrative example is presented to show that the proposed techniques are easily applied in practice.