A Bayesian Decision Theory Approach to Classification Problems

Abstract

We address the classification problem where an item is declared to be from populationπjif certain of its characteristicsvare assumed to be sampled from the distribution with pdf fj(v∣θj), wherej=1, 2, …, m. We first solve the two population classification problem and then extend the results to the generalmpopulation classification problem. Usually only the form of the pdf's is known. To use the classical classification rule the parameters,θj, must be replaced by their estimates. In this paper we allow the parameters of the underlying distributions to be generated from prior distributions. With this added structure, we obtain Bayes rules based on predictive distributions and these are completely determined. Using the first-order expansion of the predictive density, where the coefficients of powers ofn−1remain uniformly bounded innwhen integrated, we obtain an asymptotic bound for the Bayes risk.