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September, 1984 A Characterization Theorem for Externally Bayesian Groups
Christian Genest
Ann. Statist. 12(3): 1100-1105 (September, 1984). DOI: 10.1214/aos/1176346726

Abstract

A contribution is made to the problem of combining the subjective probability density functions $f_1, \cdots, f_n$ of $n$ individuals for some parameter $\theta$. More precisely, the situation is addressed which occurs when the members of a group share a common likelihood for some data and want to ensure that combining their posterior distributions for $\theta$ will yield the same result obtained by applying Bayes' rule to the aggregated prior distribution. Under certain regularity conditions to be discussed below, the logarithmic opinion pool $\prod^n_{i=1} f^{w_i}_i \big/ \int \prod^n_{i=1} f^{w_i}_i d\mu$ with $w_i \geq 0$ and $\sum^n_{i=1} w_i = 1$ is shown to be the only pooling formula which satisfies this criterion of group rationality.

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Christian Genest. "A Characterization Theorem for Externally Bayesian Groups." Ann. Statist. 12 (3) 1100 - 1105, September, 1984. https://doi.org/10.1214/aos/1176346726

Information

Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0541.62003
MathSciNet: MR751297
Digital Object Identifier: 10.1214/aos/1176346726

Subjects:
Primary: 62A99
Secondary: 39B40

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • September, 1984
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