On information and priors: a synthesis

Abstract

This work is organized as follows. In section 2, we will introduce an indexed family of information functionals. In section 3, on the basis of asymptotic normality, we will state a relationship between Bernardo's (1979) criterion functional and some members of the indexed family. In section 4, we will study a Bayesian inference problem associated with convex combinations of relevant members of the proposed indexed family. Here, we will introduce Good-Bernardo-Zellner's priors as well as their controlled versions as solutions of maximizing discounted entropy. We will give special attention to the existence and uniqueness of the solution of the corresponding optimization problems. In section 5, we will study Good-Bernardo-Zellner's priors as Kalman Filtering priors. Finally, in section 6, we will give conclusions, acknowledge limitations, and make suggestions for future research.