The Theory of Signal Detectability: Bayesian Philosophy, Classical Statistics, and the Composite Hypothesis

摘要

Receiver design and performance from a Bayesian viewpoint depend upon a priori specification whenever unknown parameters are encountered in the detection situation; any available information is expressed in the form of an a priori density. A sensitivity index is developed which measures the performance loss that occurs when the receiver is designed to be optimal with respect to the given a priori density g(.) but operates in an environment in which the a priori density h(.) is considered to hold. A comparison of receiver performance is made for the composite hypothesis situation. The Bayesian approach is contrasted to the classical approach. Initial indications were that classical statistics could be closely linked to Bayesian philosophy since analysis according to either mode ofter led to the same receiver. It appeared that many of the classical tests could be generated from a Bayesian viewpoint by an appropriate assignment of the a priori density. Investigation revealed that this was not true in general; and the conclusion is drawn that the Bayesian approach is uniquely distinct from the classical approach. The externally sensed parameter receiver is reviewed and its receiver operating characteristic is evaluated for several examples not considered before. Receiver design via numerical integration techniques is demonstrated to be feasible for composite hypothesis situations previously considered too complex to solve. Receiver design via estimation techniques is considered justifiable in case optimal procedures are too complex. (Author)