Neutral-data comparisons for Bayesian testing

Abstract

A novel approach to evidence assessment in Bayesian hypothesis testing is proposed, in the form of a "neutral-data comparison." The proposed assessment is similar to a Bayes factor, but, rather than comparing posterior to prior odds, it compares the posterior odds of the observed data to that calculated on "neutral" data, which arise as part of the elicitation of prior knowledge. The article develops a general theory of neutral-data comparisons, motivated largely by the Jeffreys-Lindley paradox, and develops methodology for specifying and working with neutral data in the context of Gaussian linear-models analysis. The proposed methodology is shown to exhibit exceptionally strong asymptotic-consistency properties in high dimensions, and, in an application example, to accommodate challenging analysis objectives using basic computational algorithms.