Analytical derivation of the reference prior by sequential maximization of Shannon's mutual information in the multi-group parameter case

Abstract

We provide an analytical derivation of a non-informative prior by sequential maximization of Shannon's mutual information in the multi-group parameter case assuming reasonable regularity conditions. We show that the derived prior coincides with the reference prior proposed by Berger and Bernardo, and that it can be considered as a useful alternative expression for the calculation of the reference prior. In using this expression we discuss the conditions under which an improper reference prior can be uniquely defined, i.e. when it does not depend on the particular choice of nested sequences of compact subsets of the parameter space needed for its construction. We also present the conditions under which the reference prior coincides with Jeffreys' prior.