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.
翻译:我们研究了巴耶斯M-ary假设测试的变式,在测试中,处理观察后,L候选者清单在M 可能范围内产生。我们研究了列表假设测试的最低误差概率,其中错误的定义是真实假设不在试验列表输出中的事件。我们得出了最小概率或误差的两个确切表达方式。第一个表达方式是某些非巴伊西亚双子假设测试的误差概率,并且是元反线的回象。第二个表达方式是上述非巴伊西亚双子假设测试所涉及的两种分布概率的尾端概率。