Reconciling Bayesian and Frequentist Evidence in the One-Sided Scale Parameter Testing Problem

• Activity Number: 292
• Type: Contributed
• Date/Time: Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Athanasios Micheas*+ and Dipak Dey
• Companies: University of Missouri-Columbia and University of Connecticut
• Keywords: Bayesian p-values ; posterior probability ; predictive distribution ; prior distribution

Abstract

An interesting but controversial problem arises when Bayesian as well as frequentist methodologies suggest very often similar solutions. For over two decades, there has been an effort by several authors to assess when Bayesian and frequentist methods provide exactly the same answers when employed. We encounter this situation in the problem of hypothesis testing, where Bayesian evidence, such as Bayes factors and prior or posterior predictive p-values are set against the classical p-value. In this paper, we develop prior predictive and posterior predictive p-values for one sided hypothesis testing scale parameter problems. We reconcile Bayesian and frequentist evidence by showing that for many classes of prior distributions, the infimum of the prior predictive and posterior predictive p-values are equal to the classical p-value. The results are illustrated through standard examples.