Cost evaluation of a two-stage classification procedure

A two-stage classification rule is suggested for classifying an individual into one of two multivariate normal populations. An individual may be classified using measurements on just the first subset; otherwise the second subset is measured and he is classified using the combined set. On the basis of misclassification costs and costs of collecting observations, the two-stage rule is compared with the usual rules based on the first subset and on the combined set. Comparisons are made for the case of known population parameters and also for the case of unknown population parameters which are estimated from samples. It is assumed throughout that a priori probabilities, cost of misclassification, and cost of making observation are known.