Abstract: This paper is devoted to study of characteristics of logarithmically asymptotically optimal (LAO)
hypotheses testing and identification for a model consisting of two related objects. In general case it is supposed
that L1 possible probability distributions of states constitute the family of possible hypotheses for the first object
and the second object is distributed according to one of L1 × L2 given conditional distributions depending on the
distribution index and the current observed state of the first object. For the first testing procedure the matrix of
interdependencies of all possible pairs of the error probability exponents (reliabilities) in asymptotically optimal
tests of distributions of both objects is studied. The identification of the distributions of two objects gives an
answer to the question whether 1
r -th and 2r -th distributions occurred or not on the first and the second objects,
correspondingly. Reliabilities for the LAO identification are determined for each pair of double hypotheses. By the
second approach the optimal interdependencies of lower estimates of all possible pairs of corresponding
reliabilities are found and lower estimates of reliabilities for the LAO identification are studied for each pair of
hypotheses. The more complete results are presented for model of statistically dependent objects, when
distributions of the objects are dependent, but its current states are independent. For an example of two
statistically dependent objects optimal interdependencies of pairs of reliabilities are calculated and graphically
presented.

Keywords: Multiple hypotheses testing, Identification of distribution, Inference of many objects, Error probability
exponents, Reliabilities.

Link:

ON RELIABILITY APPROACH TO MULTIPLE HYPOTHESES TESTING AND TO
IDENTIFICATION OF PROBABILITY DISTRIBUTIONS OF TWO STOCHASTICALLY
RELATED OBJECTS

Evgueni Haroutunian, Aram Yessayan, Parandzem Hakobyan

http://www.foibg.com/ijita/vol17/ijita17-3-p06.pdf