Bayesian Inference on Finite Mixtures of Poisson Distributions

Abstract

Mixed Poisson distributions are widely used in various disciplines to model data in which each observation is assumed to come from one of a number of Poisson distributions with different parameters. In this thesis, we investigate the Bayesian estimation for the finite Poisson mixture model using the Gibbs sampler as an important one of the MCMC methods. Our approach in this thesis depends on using the Gibbs sampler to simulate a Markov chain which has the posterior density as its stationary distribution. Then we use the resulting sample to make the suitable Bayesian computations and draw conclusion about the unknown parameters of the Poisson mixture model. We conclude this thesis by presenting a real data example to illustrate our methodology.