Objective Bayesian testing and model selection for Poisson models.

摘要

Count data may be related to covariates and exposures via a Poisson regression model. This study is concerned with the objective Bayesian approach to testing hypotheses and model selection for Poisson models. When little or no prior information is available, use of an objective (or default) prior is often considered desirable. We review and develop several objective priors; included here are such recently developed techniques as shrinkage priors, fractional priors, intrinsic priors. The characteristics of these priors are evaluated in terms of what may be regarded as desirable of objective priors for testing and model selection. Since objective priors for a given problem can be used automatically in different applications involving the same problem, it may also be of interest to compare the frequentist probabilities of wrong decisions associated with the use of these priors. In this research, we also propose and investigate the shrinkage priors and default conjugate priors for the parameters in Poisson Generalized Linear Mixed Models. Chib's approach in the context of MCMC is used for estimating the marginal likelihood for the purpose of Bayesian model comparisons, especially when the computation is complex.