Bayes Factors for Linear and Log‐Linear Models with Vague Prior Information

Summary The Bayes factor, or integrated likelihood ratio, provides a possible Bayesian alternative to the standard F ‐test procedure for comparing two linear models. However, if vague prior information for the model parameters is represented by limiting improper prior forms, it is well known that the resulting Bayes factor involves an arbitrary, unspecified constant, and is thus not well defined. A method of assigning this constant is proposed and illustrated for a number of standard problems. The approach is then extended to the analysis of contingency tables using log‐linear models.