Coherent Measures of Discrepancy, Uncertainty and Dependence, with Applications to Bayesian Predictive Experimental Design

Abstract

We show how, associated with any decision problem, we may derive related functions measuring uncertainty, discrepancy and dependence of distributions. Such "coherent" functions have special properties, which we characterise, and each function essentially determines the others. The theory is applied to the Bayesian formulation of the problem of choosing an experiment in order to make a subsequent prediction. It is shown that coherent choice criteria may be based on any of the coherent functions, with related functions yielding identical solutions.

arXiv commentThis is an old unpublished paper--Research report 139 (1994) of the Department of Statistical Science, University College London, updated 1998--that many people have asked to be made available online