Intrinsic Priors for Model Selection Using an Encompassing Model with Applications to Censored Failure Time Data

In Bayesian model selection or testingproblems one cannot utilize standard or default noninformativepriors, since these priors are typically improper and are definedonly up to arbitrary constants. Therefore, Bayes factors andposterior probabilities are not well defined under these noninformativepriors, making Bayesian model selection and testing problemsimpossible. We derive the intrinsic Bayes factor (IBF) of Bergerand Pericchi (1996a, 1996b) for the commonly used models in reliabilityand survival analysis using an encompassing model. We also deriveproper intrinsic priors for these models, whose Bayes factors are asymptoticallyequivalent to the respective IBFs. We demonstrate our resultsin three examples.