MULTIPLE BAYES FACTORS FOR TESTING HYPOTHESES

Partial and multiple Bayes factors are introduced to obtain pairwise comparisons of hypotheses in a statistical experiment with a partition on the parameter space. Robust Bayesian analyses are performed by introducing suitable classes of priors and by calculating lower and upper bounds of Bayes factors and posterior probabilities. Classes of intuitively meaningful priors are introduced, including unimodal densities without the constraint of symmetry for the case of precise hypotheses. Procedures for the corresponding optimizations are specified, and examples are given.