On a property of probability matching priors: matching the alternative coverage probabilities

Abstract

SUMMARY In frequentist inference based on confidence sets, both the true coverage and the probability for a confidence set to include an alternative value of the parameter of interest are important. Thus if probability matching priors also match such alternative coverage probabilites there is perhaps a stronger justification for calling them noninformative. Considering contiguous alternatives, we obtain the relevant necessary and sufficient conditions. In particular, with n denoting the sample size, it is seen that probability matching priors up to o(n-2) also match the alternative coverage probabilities up to that order while this is not necessarily the case with probability matching priors up to o(n-').