Behavioral Utility-Based Distributed Detection With Conditionally Independent Observations

This paper establishes a mathematical framework to analyze the behavioral utility-based distributed detection problem for $M$-ary hypothesis testing with conditionally independent observations at the local decision agents (DAs). It is assumed that a human acts as the fusion center (FC) and his subjective perception of probabilities and gains/losses are considered using a prospect theoretic approach. In contrast with the classical Bayes risk-based approach, the nonlinear dependence of the behavioral performance metric on the likelihood functions necessitates a novel perspective to analyze the problem. Using geometric properties of the set of all possible probability distributions induced by randomized decision rules, the forms of optimal decision rules at the local DAs and the FC are characterized. In particular, it is shown that randomization between at most two distinct likelihood ratio vector quantizers, each of which partitions the nonnegative orthant into convex polytopes, attains optimal performance. The simplification to the case of binary quantization at a local DA for the binary hypothesis testing problem along with illustrative examples and performance comparisons are presented to corroborate theoretical results.