Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3386
Abstract
he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.
Keywords
List $M$-ary hypothesis testing, probability of error, lower bound, Fano's inequality
First Page
678
Last Page
686
Recommended Citation
DÜLEK, BERKAN
(2023)
"Novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 18.
https://doi.org/10.55730/1300-0098.3386
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/18
