Intrinsic priors for model selection using an encompassing model with applications to censored failure time data

In Bayesian model selection or testing problems one cannot utilize standard or default noninformative priors, since these priors are typically improper and are defined only up to arbitrary constants. Therefore, Bayes factors and posterior probabilities are not well defined under these noninformative priors, making Bayesian model selection and testing problems impossible. We derive the intrinsic Bayes factor (IBF) of Berger and Pericchi (1996a, 1996b) for the commonly used models in reliability and survival analysis using an encompassing model. We also derive proper intrinsic priors for these models, whose Bayes factors are asymptotically equivalent to the respective IBFs. We demonstrate our results in three examples.