On a Constrained Optimal Rule for Classification with Unknown Prior Individual Group Membership

We describe a formal approach to constructing the optimal classification rule for classification analysis with unknown prior probabilities ofKmultivariate normal populations membership. This is done by suggesting a balanced design for the classification experiment and by constructing the optimal rule under the balanced design condition. The rule is characterized by a constrained minimization of total risk of misclassification; the constraint of the rule is constructed by a process of equalization among expected utilities ofKpopulation conditional densities. The efficacy of the suggested rule is examined through numerical studies. This indicates that dramatic gains in the accuracy of classification result can be achieved in the case where little is known about the relative population sizes.