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

Area of Science:

• Statistics
• Bayesian Inference
• Reliability and Survival Analysis

Background:

• Standard noninformative priors in Bayesian analysis are often improper, leading to undefined Bayes factors and posterior probabilities.
• This limitation hinders Bayesian model selection and testing, particularly in specialized fields like reliability and survival analysis.

Purpose of the Study:

• To derive the intrinsic Bayes factor (IBF) for common reliability and survival analysis models.
• To develop proper intrinsic priors that yield Bayes factors asymptotically equivalent to the IBFs.
• To address the challenge of applying Bayesian model selection with noninformative priors.

Main Methods:

• Utilizing an encompassing model to derive the intrinsic Bayes factor (IBF).
• Deriving proper intrinsic priors for specific reliability and survival models.
• Employing asymptotic equivalence for validating derived priors against IBFs.

Main Results:

• Successful derivation of the intrinsic Bayes factor (IBF) for commonly used models in reliability and survival analysis.
• Development of proper intrinsic priors that provide Bayes factors asymptotically equivalent to the IBFs.
• Demonstration of the methodology through three practical examples.

Conclusions:

• The intrinsic Bayes factor and derived proper intrinsic priors provide a viable solution for Bayesian model selection in reliability and survival analysis.
• These methods overcome the limitations posed by improper noninformative priors.
• The approach is validated and applicable to real-world problems in these fields.