An alternative to minimax for designing binary decision rules

The minimax approach to designing decision rules when modeling uncertainty exists is somewhat conservative in that only the most undesirable possible conditions are taken into account. Consequently, the performance under other conditions may sometimes be poor. The segment method was introduced in the context of optimal control as an alternative to the minimax approach. The segment method takes into account the system performance over the entire range of model parameter values. In this paper the basic concept of the segment method is reviewed. The method is then applied to the design of binary decision rules under various conditions of uncertainty including unknown mean or variance for Gaussian statistics. It is shown that the segment method often results in system performance which is more attractive than the performance from the minimax design for the same problem.