Some Risks with Bayes and Some Higher-Order Truths

• Activity Number: 600
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Donald A.S. Fraser*+
• Companies: University of Toronto
• Keywords: Confidence ; Bayes ; Integrated likelihood ; Approximate confidence ; Truth

Abstract

.A.S. Fraser Dept Statistics University of Toronto

Bayesians with default priors calculate numbers that are called probabilities; non-Bayesians with more effort calculate numbers that are called confidence but by edict never called probabilities. We examine higher-order analyses that show the Bayesian numbers have less claim to truth than the confidence numbers do; and can even be uniformly biased. Integrating weighted likelihood can of course provide rich and rewarding exploratory analyses in wide generality. But the Bayesian claim of producing probabilities is demonstrably misrepresentative, even fraudulent, unless the claim is reduced to that of producing approximate confidence. Bayesian analysis is frequently described as basic information processing, but it requires a disclaimer concerning the use of the term probability over approximate confidence.