Multilevel minimax hypothesis testing

In signal detection, Bayesian hypothesis testing and minimax hypothesis testing represent two extremes in the knowledge of the prior probabilities of the hypotheses: full information and no information. We propose an intermediate formulation, also based on the likelihood ratio test, to allow for partial information. We partition the space of prior probabilities into a set of levels using a quantization-theoretic approach with a minimax Bayes risk error criterion. Within each prior probability level, an optimal representative probability value is found, which is used to set the threshold of the likelihood ratio test. The formulation is demonstrated on signals with additive Gaussian noise.