Interactive use of default and robust Bayes testing methods in the presence of vague prior information

Abstract

Summary. The paper considers the compatibility of inferences from default Bayes testing methods with robust Bayesian solutions obtained in the presence of weak prior information represented by classes of priors. Interest focuses on establishing whether, in specific problems, the observed value of a default choice criterion, such as an alternative Bayes factor or an asymptotic method such as the Bayes information criterion, falls into the range of values of the standard Bayes factor, obtained as the priors vary in the elicited classes. When this happens, the default Bayes factor is a true Bayesian solution; in addition, it provides a way to select a single value to be used as a measure of evidence, out of a wide range of solutions, given by the robust analysis. Compatibility of default and robust Bayes testing analysis is shown to hold in several problems when conjugate classes of prior are used.