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Bayesian localization of anomaly in distributed networks with quadratic criterion

The anomaly localization in distributed networks can be treated as a multiple hypothesis testing (MHT) problem and the Bayesian test with 0-1 loss function is a standard solution to this problem. However, For the anomaly localization application, the cost of different false localization varies, which cannot be reflected by the 0 - 1 loss function while the quadratic loss function is more appropriate. The main contribution of the paper is the design of a Bayesian test with a quadratic loss function and its performance analysis. The non-asymptotic bounds of the misclassification probabilities of the proposed test and the standard one with 0-1 loss function are established and the relationship between their asymptotic equivalence with respect to signal-to-noise ratio and the geometry of the parameter space is analyzed. The effectiveness of the non-asymptotic bounds and the analysis on the asymptotic equivalence are verified by the simulation results.