Theoretical Bounds in Minimax Decentralized Hypothesis Testing

TL;DR

This paper establishes theoretical bounds on the performance loss in minimax decentralized hypothesis testing, comparing scenarios with and without a fusion center, under uncertainty about the Bayesian prior.

Contribution

It derives bounds on detection performance loss in minimax decentralized detection with and without a fusion center, generalizing previous results.

Findings

Maximum loss in detection performance without a fusion center is quantified.

Maximum performance loss between networks with and without a fusion center is derived.

Results are generalized to broader scenarios.

Abstract

Minimax decentralized detection is studied under two scenarios: with and without a fusion center when the source of uncertainty is the Bayesian prior. When there is no fusion center, the constraints in the network design are determined. Both for a single decision maker and multiple decision makers, the maximum loss in detection performance due to minimax decision making is obtained. In the presence of a fusion center, the maximum loss of detection performance between with- and without fusion center networks is derived assuming that both networks are minimax robust. The results are finally generalized.