Bayesian Binary Hypothesis Testing Under Model Uncertainty
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We consider Bayesian binary hypothesis testing problem when there is only partial knowledge about one of the distributions, while the other distribution is fully known. Specifically, let P-1 and P-2 be the distributions under two hypothesis, where P-2 is known and P-1 is unknown. We propose a test and show that if the Chernoff distance between P-1 and P-2 is known to be larger than Phi, an error exponent Phi,- epsilon, epsilon > 0, can be achieved in the Bayesian setting. If the Chernoff distance between P-1 and P-2 is not known, but another distribution Q(1) known such that l(1) distance between P-1 and Q(1) is known the smaller than a, then the same test can be applied, and it coincides with the robust hypothesis testing methods existing in the literature.