On Optimal Hypothesis Testing for Pair of Stochastically Coupled Objects
The paper is devoted to hypotheses testing for a model consisting of two stochastically coupled objects. It is supposed that L1 possible probability distributions are known for the first object and the second object is distributed according to one of L1 X L2 given conditional distributions depending on the distribution index and the current observed state of the first object. The matrix of interdependencies of all possible pairs of the error probability exponents in asymptotically optimal tests of distributions of both objects is studied. The case of two objects which cannot have the same probability distribution from two possible variants was considered by Ahlswede and Haroutunian. This case for three hypotheses and the model of two statistically dependent objects for two hypotheses were examined by Haroutunian and Yessayan.
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