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July, 1974 Bayesian Classification: Asymptotic Results
C. P. Shapiro
Ann. Statist. 2(4): 763-774 (July, 1974). DOI: 10.1214/aos/1176342763

Abstract

We have a population composed of two subpopulations whose probability properties are described by known univariate distribution functions, $G(x)$ and $H(x)$, respectively. The probability of observing an individual from the first population is $\theta$, from the second is $1 - \theta$. We assume $\theta$ is a random variable with a prior distribution on (0, 1) and find the Bayes rule for classifying $n$ observations as from $G$ or from $H$ when the loss function is equal to the number of misclassifications. The main results in the paper give the asymptotic properties of the Bayes rule and several proposed approximations.

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C. P. Shapiro. "Bayesian Classification: Asymptotic Results." Ann. Statist. 2 (4) 763 - 774, July, 1974. https://doi.org/10.1214/aos/1176342763

Information

Published: July, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0286.62040
MathSciNet: MR362590
Digital Object Identifier: 10.1214/aos/1176342763

Subjects:
Primary: 62C10
Secondary: 62E20

Keywords: asymptotic distribution , Bayesian inference , ‎classification‎ , weak limit

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 4 • July, 1974
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