Abstract
In this paper, we consider the Bayesian analysis of two overdispersed Poisson models. The first is an overdispersed generalized Poisson model. The second is an ordinary Poisson and overdispersed generalized Poisson mixture model. Shoukri and Consul (1989, Comimintiicationis inz Statistics: Simnllationi anzd Comiiptutationi 18, 1465-1480) have previously considered a limited form of approximate Bayesian analysis for the first of these two models requiring the use of Pearson curves and the assumption that a certain model parameter has support on a finite number of values. By way of comparison, this paper demonstrates how a full Bayesian analysis of either model may proceed by making use of the Gibbs sampler and adaptive rejection sampling methods for log-concave densities. The methodology is illustrated with an application to a biological data set.
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