## The Annals of Statistics

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

### A Characterization Theorem for Externally Bayesian Groups

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/aos/1176346726

**Mathematical Reviews number (MathSciNet)**

MR751297

**Zentralblatt MATH identifier**

0541.62003

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62A99: None of the above, but in this section

Secondary: 39B40

**Keywords**

External Bayesianity logarithmic opinion pool consensus

#### Citation

Genest, Christian. A Characterization Theorem for Externally Bayesian Groups. Ann. Statist. 12 (1984), no. 3, 1100--1105. doi:10.1214/aos/1176346726. https://projecteuclid.org/euclid.aos/1176346726