Information measures and bayesian hierarchical models

Abstract

We consider the Bayesian statistical models in which the prior distribution of the parameter vector θ1 in the distribution of an observable random vector X is to be specified in a hierarchical fashion and one wants to learn about the hyperparameters at each level of this prior distribution. It is shown that for a wide class of information measures, based on the so-called f divergence, the information decreases as one moves to higher levels of hyperparameters. This result unifies all the theorems in Goel and DeGroot (1981) and provides several other information measures for which the above desirable property holds. © 1983 Taylor & Francis Group, LLC.