Data augmentation and Gibbs sampling for regression models of small counts

In this article we consider Bayesian analysis of Poisson regression models. Estimation is carried out within a Bayesian framework using data augmentation and MCMC methods. We suggest a new MCMC sampler, which possesses a Gibbs transition kernel, where we draw from full conditional distributions belonging to standard distribution families, only. This Gibbs sampler is applied to a standard Poisson regression model and to a Poisson regression models
dealing with overdispersion.