Hypothesis Assessment and Inequalities for Bayes Factors and Relative Belief Ratios

We discuss the definition of a Bayes factor and develop some inequalities relevant to Bayesian inferences. An approach to hypothesis assessment based on the computation of a Bayes factor, a measure of the strength of the evidence given by the Bayes factor via a posterior probability, and the point where the Bayes factor is maximized is recommended. It is also recommended that the a priori properties of a Bayes factor be considered to assess possible bias inherent in the Bayes factor. This methodology can be seen to deal with many of the issues and controversies associated with hypothesis assessment. We present an application to a two-way analysis.