Generalized performance

Abstract

The performance of a Bayes optimal detector is summarized by its ROC curve. In the general ease where uncertain parameters exist under each hypothesis, knowledge about them is explicitly noted at the outset by an a priori probability density function conditional to H1 and one conditional to H0. The processor's performance then becomes a function of their detailed shape. Often, the functional form of these densities is chosen so that various levels of uncertainty are easily modeled and a family of ROC's is reported. The question then arises: What performance would have been achieved under different prior knowledge assumptions (particularly when outside the class of densities modeled)? Or, more deeply: Does some algorithm exist which will operate on a known ROC for a given pair of priors to yield the ROC for a new set of priors? And, if not: Does a canonical intermediate step exist between observation and likelihood ratio statistics which always may be used as a starting point for the calculation of an ROC based on an arbitrary pair of priors? The intent of this paper is to pursue these questions. The discussion will use as a basis the fundamental concepts of sufficient statistics and reproducing densities. A specific example is presented. [Work supported by ONR.]