On minimum information prior distributions

Abstract

The formulation of the concept of non-informative prior distribution over a finite number of possibilities is considered and the minimum information prior distribution is defined as the prior distribution that adds minimum expected amount of information to the posterior distribution. Numerical examples show that the definition leads to nontrivial results. An information inequality is established to assure the validity of numerical results. The relation of the present work to other works on the same subject is briefly reviewed and finally a minimax type prior distribution is introduced that exhibits the impartial property which is lacking in the minimum information prior distribution.