Title :
A general class of lower bounds on the probability of error in multiple hypothesis testing
Author :
Routtenberg, Tirza ; Tabrikian, Joseph
Author_Institution :
Dept. of Electr. & Comput. Eng., Ben-Gurion Univ. of the Negev, Beer-Sheva, Israel
Abstract :
In this paper, a new class of lower bounds on the probability of error for m-ary hypothesis tests is proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion, is usually not tractable. The new class is derived using Holder¿s inequality. The bounds in this class are continuous and differentiable function of the conditional probability of error and they provide good prediction of the minimum probability of error in multiple hypothesis testing. It is shown that for binary hypothesis testing problem this bound asymptotically coincides with the optimum probability of error provided by the MAP criterion. This bound is compared with other existing lower bounds in several typical detection and classification problems in terms of tightness and computational complexity.
Keywords :
computational complexity; error statistics; maximum likelihood estimation; statistical testing; Holder inequality; computational complexity; conditional probability; error probability; m-ary hypothesis tests; maximum a-posteriori probability; minimum probability; multiple hypothesis testing; Bayesian methods; Computational complexity; Computer errors; Entropy; Error probability; Maximum a posteriori estimation; Performance analysis; Statistical distributions; System analysis and design; Testing; MAP; detection; hypothesis testing; lower bounds; probability of error;
Conference_Titel :
Electrical and Electronics Engineers in Israel, 2008. IEEEI 2008. IEEE 25th Convention of
Conference_Location :
Eilat
Print_ISBN :
978-1-4244-2481-8
Electronic_ISBN :
978-1-4244-2482-5
DOI :
10.1109/EEEI.2008.4736635
