Authors
Jian Zhang, Lionel Fillatre, Igor Nikiforov,
Title
Bayesian test for multiple hypothesis testing problem with quadratic loss
In
11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing
Volume
11
Issue
Part 1
Pages
506–511
Publisher
International Federation of Automatic Control
Year
2013
Indexed by
Abstract
The Bayesian test with 0-1 loss function is a standard solution to solve a multiple hypothesis testing problem in the Bayesian framework. For a large number of applications (like the intrusion detection, the anomaly detection,...) the alternative hypotheses have quite different importance and 0-1 loss function does not reflect the reality. The quadratic loss function can be more appropriate to distinguish the concurrent hypotheses. The main contribution of the paper is the design of the Bayesian test with a quadratic loss function and its asymptotic study. When the signal-to-noise ratio tends to infinity, it is theoretically established that the error probabilities of the proposed test coincide with the error probabilities of the standard one associated to the 0-1 loss function. In the non-asymptotic case, the numerical experiments show that the proposed test outperforms the Bayesian test associated to the 0-1 loss function when compared by using the quadratic loss function.
Affiliations
Offprint