Minimum Probability of Error of List Mary Hypothesis Testing
Abstract
We study a variation of Bayesian Mary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an error is defined as the event where the true hypothesis is not in the list output by the test. We derive two exact expressions of the minimum probability or error. The first is expressed as the error probability of a certain nonBayesian binary hypothesis test, and is reminiscent of the metaconverse bound. The second, is expressed as the tail probability of the likelihood ratio between the two distributions involved in the aforementioned nonBayesian binary hypothesis test.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.14608
 Bibcode:
 2021arXiv211014608A
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Statistics Theory
 EPrint:
 11 pages, submitted to Information and Inference: a journal of the IMA