  The Poisson distribution is often used as a standard model for count data.
Quite often, however, such data sets are not well fit by a Poisson model
because they have more zeros than are compatible with this 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 include covariates in regression models. Several applications are
given.
