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    Hypotheses optimal testing via large deviations techniques
    (Maltepe Üniversitesi, 2009) Navaei, Leader
    The problem of many hypotheses testing for a model consisting of L > 2 hypotheses on distribution of a Markov chain is studied. We apply large deviations techniques (LDT) and the method of types to the empirical distributions of finite states of Markov chain. It is proved that this method of investigation in solving the problem of logarithmically asymptotically optimal (LAO) hypotheses testing is easier than the procedure that was introduced by Haroutunian. The matrix of exponents E = {El|m}, m, l = 1, L of error probabilities of the LAO test El|m(?) = lim N?? ? 1 N log ?l|m(?N ), where ? N l|m(?N ) for l 6= m is the probability to accept the hypothesis l, when the hypothesis m is true, is determined.
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    On identification of distribution for two independent markov chains to the subject reliability criterion
    (Maltepe Üniversitesi, 2009) Navaei, Leader
    Ahlswede and Haroutunian in [1] formulated an ensemble of problems on multiple hypotheses testing for many objects and on identification of hypotheses under reliability requirement. The problem of many (L > 2) hypotheses testing on distributions of a finite state Markov chain is studied in [5] via large deviations techniques. In this paper we solve the problem to identification of distributions of many hypotheses for two independent objects by usage of simple homogeneous stationary finite states of Markov chains.
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    On identification of distributions for multiple lao hypotheses testing
    (Maltepe Üniversitesi, 2009) Navaei, Leader
    Applications of information-theoretical methods in mathematical statistics are reflected in the monographs by Kullback [5], Csisz´ar and K¨orner [2], Gutman [3] and others. In [1] Ahlswede and Haroutunian formulated an ensemble of new problems on multiple hypotheses testing for many objects and on identification of hypotheses. The problem of many (L > 2) hypotheses testing on distributions of a finite state Markov chain is studied in [6] via large deviations techniques. In this paper we solve the problem to identification of distributions of many hypotheses for one object by usage of simple homogeneous stationary finite states of Markov chains.