We address the classification problem where an item is declared to be from population ? j if certain of its characteristics v are assumed to be sampled from the distribution with pdf f j (v | % j ), where j=1, 2, ..., m. We first solve the two population classification problem and then extend the results to the general m population classification problem. Usually only the form of the pdf's is known. To use the classical classification rule the parameters, % j , 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 of n &1 remain uniformly bounded in n when integrated, we obtain an asymptotic bound for the Bayes risk.
1996 Academic Press, Inc. is based on the ratio of the true, but unknown densities [2]. The two approaches are compared in the normal case, by Aitchison, Habbema, and Kay [1]. Kendall, Stuart, and Ord [7] also present the normal theory predictive approach.