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We study a variation of Bayesian M-ary hypothesis testing in which the testoutputs a list of L candidates out of the M possible upon processing theobservation. 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 thelist output by the test. We derive two exact expressions of the minimumprobability or error. The first is expressed as the error probability of acertain non-Bayesian binary hypothesis test, and is reminiscent of themeta-converse bound. The second, is expressed as the tail probability of thelikelihood ratio between the two distributions involved in the aforementionednon-Bayesian binary hypothesis test.

Minimum Probability of Error of List M-ary Hypothesis Testing