Affiliations: [a] School of Automation, Wuhan University of Technology, Wuhan, China
| [b] I3S Laboratory, University of Nice Sophia-Antipolis, Sophia Antipolis, France
| [c] Laboratory of Systems Modelling and Dependability, Charles Charles Institute, University of Technology of Troyes, Troyes, France
Correspondence:
[*]
Corresponding author. Jian Zhang, School of Automation, Wuhan University of Technology, 205, Luoshi Street,
430070 Wuhan, China. Tel.: +86 152 0716 4256; Fax: +86 027 8785 9049; E-mail: [email protected].
Abstract: 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.
