Bayesian Test with Quadratic Criterion for Multiple Hypothesis Testing Problem

A Bayesian test has been previously proposed for a multiple hypothesis testing (MHT) problem with a quadratic loss function such that this problem can fit with some real applications where the concurrent hypotheses should be distinguished. However, this MHT problem as well as this quadratic loss function are insufficient for some other applications such as the simultaneous intrusion detection and localization in a wireless sensor network (WSN). This kind of applications could be considered as a MHT problem with null hypothesis. Therefore, a Bayesian test with a modified quadratic loss function is proposed to solve this MHT problem. The non-asymptotic bounds for analyzing the performance of the proposed test and the Bayesian test with the 0-1 loss function are obtained, from which the conditional asymptotic equivalence between these two tests is then theoretically established. The effectiveness of these bounds and the analysis on the conditional asymptotic equivalence are verified by the simulation results.