Consistency and strong inconsistency of group-invariant predictive inferences

Abstract

Consider a statistical model which is invariant under a group of transformations that acts transitively on the parameter space. In this situation, the problem of constructing invariant predictive distributions is considered. It is shown, under certain assumptions, that Fisherian pivoting and the use of right Haar measure as an improper prior distribution both yield the same invariant predictive distribution. Furthermore, it is shown that any other invariant predictive distribution is strongly inconsistent in the sense of Stone.