A general class of lower bounds on the probability of error in multiple hypothesis testing

Abstract

In this paper, a new class of lower bounds on the probability of error for m-ary hypothesis tests is proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion, is usually not tractable. The new class is derived using Holder¿s inequality. The bounds in this class are continuous and differentiable function of the conditional probability of error and they provide good prediction of the minimum probability of error in multiple hypothesis testing. It is shown that for binary hypothesis testing problem this bound asymptotically coincides with the optimum probability of error provided by the MAP criterion. This bound is compared with other existing lower bounds in several typical detection and classification problems in terms of tightness and computational complexity.