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Large deviations for Bayes discrimination of a finite number of simple hypotheses

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Abstract

We consider the problem of discrimination of a finite number of simple hypotheses in the general scheme of statistical experiments. Under conditions of the validity of theorems on large deviations for the logarithm of likelihood ratio, we investigate the asymptotic behavior of probabilities of errors of the Bayes criterion. We obtain the asymptotics of the amount of Shannon information contained in an observation and in the Bayes criterion.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    Yu. N. Lin’kov & L. A. Gabriel’

Authors
  1. Yu. N. Lin’kov
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  2. L. A. Gabriel’
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1360–1367, October, 1999.

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Lin’kov, Y.N., Gabriel’, L.A. Large deviations for Bayes discrimination of a finite number of simple hypotheses. Ukr Math J 51, 1534–1542 (1999). https://doi.org/10.1007/BF02981686

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  • DOI: https://doi.org/10.1007/BF02981686

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