Bayes Factors Based on Test Statistics

Abstract

Summary Traditionally, the use of Bayes factors has required the specification of proper prior distributions on model parameters that are implicit to both null and alternative hypotheses. I describe an approach to defining Bayes factors based on modelling test statistics. Because the distributions of test statistics do not depend on unknown model parameters, this approach eliminates much of the subjectivity that is normally associated with the definition of Bayes factors. For standard test statistics, including the χ2-, F-, t- and z-statistics, the values of Bayes factors that result from this approach have simple, closed form expressions.