Lower bounds on Bayes factors for invariant testing situations

Hypothesis testing problems are studied when invariance under suitable groups of transformations exist. Both compact and locally compact groups are considered. Expressions for the lower bounds on Bayes factors are derived under fairly general conditions. It is shown that the lower bounds can be obtained from weighted likelihood ratios of maximal invariants. These lower bounds are then compared with the P-values for these tests. It is found that the lower bounds are usually much larger than the corresponding P-values.