Bayesian Analysis of Finite Poisson Mixtures

Finite Poisson mixtures are widely used to model overdispersed data sets for which the simple Poisson distribution is inadequate. Such data sets are very common in real applications. In this paper we investigate Bayesian estimation via MCMC for finite Poisson mixtures and we discuss some computational issues. The related problem of determining the number of components in a mixture is also treated. This problem is of particular interest since it can reveal the number of subpopulations comprising the entire population under study. We model the number of components k as a random quantity having itself a prior probability function and then we apply the Reversible Jump Markov Chain Monte Carlo (Green 1995) to estimate the number of components. A real data example dealing with a financial credit scoring system illustrates our methodology.