Optimal Detection for a Prospect Theoretic Variant of the Neyman-Pearson Problem

A prospect theoretic variant of the Neyman-Pearson (NP) detection problem is proposed for a behavioral (human) decision maker, who perceives distorted versions of the detection and false alarm probabilities. The perceived probabilities are obtained as strictly monotonic transformations of the true probabilities via a probability weighting function employed in prospect theory. It is assumed that the the decision maker can employ time-sharing among a number of detectors in order to maximize the average perceived detection probability subject to a constraint on the average perceived false alarm probability. It is shown that time-sharing between at most two distinct NP decision rules is optimal. A sufficient condition for improvability of the detection performance via time-sharing is presented based on the convexity properties of the transformed version of the receiver operating characteristic curve corresponding to the likelihood ratio detector. Numerical examples are provided to corroborate the theoretical results.