Bayesian interpretation of the partial area under the ROC, with applications to spectrum sensing

The Receiver Operating Characteristic ROC is a fundamental concept for detection in spectrum sensing and other applications. The Area Under The Curve, AUC, or integrated ROC, is a detection metric, derived from the ROC, that has been recently applied signal processing problems in cognitive radio. We present a novel interpretation of the partial AUC, in which the a priori probability of the false alarm probability is introduced, which generalizes the classical PAUC concept. Further, we show that adaptive threshold detectors, often introduced for holding a constant false alarm rate, have identical average detection performance as the PAUC. This provides a new interpretation of both the PAUC and many CFAR tests. We apply the beta prior to obtain closed-form results. Finally, Monte Carlo estimation is discussed.