Lower bounds on Bayes factors for invariant testing situations (Q1824308)

Expressions are obtained for the lower bounds of Bayes factors or weighted likelihood ratios for testing hypotheses. They are derived under the assumption that the priors or weight functions are invariant under compact and locally compact groups of transformations by using weighted likelihood ratios of maximal invariants. Lower bounds of the posterior probabilities of null hypotheses are compared with p-values and are shown to be higher in most examples presented.