The Annals of Statistics

A Characterization Theorem for Externally Bayesian Groups

Christian Genest

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.

Article information

Source
Ann. Statist. Volume 12, Number 3 (1984), 1100-1105.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176346726

Digital Object Identifier
doi:10.1214/aos/1176346726

Mathematical Reviews number (MathSciNet)
MR751297

Zentralblatt MATH identifier
0541.62003

JSTOR