Default Bayesian Testing for the Zero-in ated Poisson Distribution

Abstract

In a Bayesian model selection and hypothesis testing, users should be cautious when choosing suitable prior distributions, as it is an important problem. More often than not, objective Bayesian analyses utilize noninformative priors such as Jeffreys priors. However, since these noninformative priors are often improper, the Bayes factor associated with these improper priors is not well-defined. To circumvent this indeterminate issue, the Bayes factor can be corrected by intrinsic and fractional methods. These adjusted Bayes factors are asymptotically equivalent to the ordinary Bayes factors calculated with proper priors, called intrinsic priors. In this article, we derive intrinsic priors for testing the point null hypothesis under a zero-inflated Poisson distribution. Extensive simulation studies are performed to support the theoretical results on asymptotic equivalence, and two real datasets are analyzed to illustrate the methodology developed in this paper.