Application of Bayesian Decision Theory to Constrained Classification Networks

Abstract

A classification network of classifying subjects as either suitable or un­suitable for a treatment followed by classifying accepted subjects as either a master or nonmaster will be formalized in the case of several relevant subpopulations. It will further be assumed that only a fixed number of subjects can be accepted for the treatment. The purpose of this paper is to optimize simultaneously this constrained classification network using Bayesian decision theory. In doing so, important distinctions will be made between weak and strong as well as monotone and nonmonotone decision rules. Also, a theorem will be given under what conditions optimal (weak) rules will be monotone.