Type-based robust Bayesian hypothesis testing

There are optimum methods in Bayesian hypothesis testing for cases where probability distributions are known, but these methods are sensitive to deviations in distributions. Since probability distributions cannot be known in practical applications, it is imperative to use robust algorithms to this uncertainty. In this thesis, robust Bayesian hypothesis tests that can be used in practical applications are presented. We consider the case where the true distributions of the hypothesis are not known, but nominal distributions as close as \epsilon at the l_1 distance to these distributions are known. The type-based methods are presented for binary and multiple alphabets. In addition, the error probability upper bounds of the tests are shown. Binary hypothesis testing is introduced in two cases: one of the distributions is partially known when the true distribution of the other one is known, and both distributions are partially known. In the presented robust Bayesian hypothesis tests, the rounding operation of distributions is proposed. Also, DGL method which is the only method for multiple hypothesis testing in literature is compared with the proposed method, and it was shown by Monte Carlo simulations that the presented method provided better performance in \epsilon\rightarrow0 cases. Keywords: Bayesian hypothesis testing, method of types, robust hypothesis testing, multiple hypothesis testing, Chernoff distance