The Annals of Statistics

Modeling Expert Judgments for Bayesian Updating

Christian Genest and Mark J. Schervish

Full-text: Open access

Abstract

This paper examines how a Bayesian decision maker would update his/her probability $p$ for the occurrence of an event $A$ in the light of a number of expert opinions expressed as probabilities $q_1, \cdots, q_n$ of $A$. It is seen, among other things, that the linear opinion pool, $\lambda_0p + \sum^n_{i = 1} \lambda_iq_i$, corresponds to an application of Bayes' Theorem when the decision maker has specified only the mean of the marginal distribution for $(q_1, \cdots, q_n)$ and requires his/her formula for the posterior probability of $A$ to satisfy a certain consistency condition. A product formula similar to that of Bordley (1982) is also derived in the case where the experts are deemed to be conditionally independent given $A$ (and given its complement).

Article information

Source
Ann. Statist. Volume 13, Number 3 (1985), 1198-1212.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349664

Digital Object Identifier
doi:10.1214/aos/1176349664

Mathematical Reviews number (MathSciNet)
MR803766

Zentralblatt MATH identifier
0609.62007

JSTOR
links.jstor.org

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62A15

Keywords
Bayesian inference consensus expert opinions linear opinion pool logarithmic opinion pool

Citation

Genest, Christian; Schervish, Mark J. Modeling Expert Judgments for Bayesian Updating. Ann. Statist. 13 (1985), no. 3, 1198--1212. doi:10.1214/aos/1176349664. https://projecteuclid.org/euclid.aos/1176349664


Export citation