Objective Bayes testing of Poisson versus inflated Poisson models

The Poisson distribution is often used as a standard probability model for data involving counts. Quite often, however, such datasets are not well fit by a Poisson model because they contain more zero counts than are compatible with the Poisson model. For these situations, a zero-inflated Poisson (ZIP) distribution is often proposed. This article addresses testing a Poisson versus a ZIP model, using Bayesian methodology based on suitable objective priors. Specific choices of objective priors are justified and their properties investigated. The methodology is extended to testing Poisson versus ZIP regression models which include covariates. Several applications are given.