A note on Bayes detection of signals

The general Bayes decision rule is derived, showing that the best decision rule is always the single decision with smallest expected cost. The likelihood function detector for multiple signal classes is extended to include over lapping signal classes which occur in adaptive detection and in detection of stochastic signals. Specification of a multiple-signal detector in terms of its error probabilities is discussed, and generalizations of the Ideal Observer and the Neyman-Pearson detector are obtained.