The Annals of Statistics

Modeling Expert Judgments for Bayesian Updating

Christian Genest and Mark J. Schervish

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Bayesian inference consensus expert opinions linear opinion pool logarithmic opinion pool


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

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