2021/10/27 by Ehsan Asadi Kangarshahi, Kangarshahi, Ehsan Asadi, Albert Guillen Fabregas +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2110.14608
openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a variation of Bayesian M-ary 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 non-Bayesian binary hypothesis test, and is reminiscent of the meta-converse bound. The second, is expressed as the tail probability of the likelihood ratio between the two distributions involved in the aforementioned non-Bayesian binary hypothesis test.