On the converse theorem in statistical hypothesis testing

Discussion on the converse theorem in statistical hypothesis testing. Hypothesis testing for two Markov chains is considered. Under the constraint that the first-kind error probability is less than or equal to exp( T R ), the second-kind error probability is minimized. The geodesic that connects the two Markov chains is defined. By analyzing the geodesic, the power exponents are calculated and then represent in terms of Kullback-Leibler divergence. Zndex TermsHypothesis testing, Markov chain, randomized test, information geometry, geodesic, power exponent, converse theorem.