The Annals of Mathematical Statistics

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

Morton Kupperman

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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.

Article information

Source
Ann. Math. Statist., Volume 29, Number 2 (1958), 571-575.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706633

Digital Object Identifier
doi:10.1214/aoms/1177706633

Mathematical Reviews number (MathSciNet)
MR100937

Zentralblatt MATH identifier
0087.14402

JSTOR
links.jstor.org

Citation

Kupperman, Morton. Probabilities of Hypotheses and Information-Statistics in Sampling from Exponential-Class Populations. Ann. Math. Statist. 29 (1958), no. 2, 571--575. doi:10.1214/aoms/1177706633. https://projecteuclid.org/euclid.aoms/1177706633


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Corrections

  • See Correction: Morton Kupperman. Correction to "Probabilities of Hypotheses and Information-Statistics in Sampling From Exponential-Class Populations". Ann. Math. Statist., Vol. 29, Iss. 4 (1958) 1278.