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Probabilities of Hypotheses and Information-Statistics in Sampling from Exponential-Class Populations

Morton Kupperman
The Annals of Mathematical Statistics
Vol. 29, No. 2 (Jun., 1958), pp. 571-575
Stable URL: http://www.jstor.org/stable/2237349
Page Count: 5
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Probabilities of Hypotheses and Information-Statistics in Sampling from Exponential-Class Populations
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Abstract

This paper is concerned with inequalities connecting probabilities of hypotheses using Bayes' theorem (a posteriori probabilities), a priori probabilities, and Kullback-Leibler information-statistics in sampling from populations belonging to the exponential class of populations. As a corollary, it is shown that if it is known that the a priori probabilities are all equal, the choice of the hypothesis with the minimum Kullback-Leibler information-statistic is the same as the choice of the hypothesis with the maximum a posteriori probability, and conversely.

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