Intrinsic priors for comparing zero-inflation parameters in Poisson models

Prior elicitation is an important issue in both objective and subjective Bayesian inferences. In hypothesis testing and model selection, choosing appropriate prior distributions becomes significantly more critical. In an objective Bayesian analysis, one utilizes noninformative priors such as Jeffreys priors or reference priors for hypothesis testing which are often improper, making unspecified constants to be contained in the Bayes factor. Thus, the resulting Bayes factor should be adjusted. In this paper, we consider default Bayes procedures for testing zero-inflation parameters in a zero-inflated Poisson distribution. In particular, we derive a set of intrinsic priors based on an approximation procedure. Extensive simulations and analyses of two real datasets are performed to support the methodology developed in the paper. It is shown that the proposed Bayesian and frequentist approaches yield similar comparable results.