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September, 1985 Modeling Expert Judgments for Bayesian Updating
Christian Genest, Mark J. Schervish
Ann. Statist. 13(3): 1198-1212 (September, 1985). DOI: 10.1214/aos/1176349664


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).


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Christian Genest. Mark J. Schervish. "Modeling Expert Judgments for Bayesian Updating." Ann. Statist. 13 (3) 1198 - 1212, September, 1985.


Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0609.62007
MathSciNet: MR803766
Digital Object Identifier: 10.1214/aos/1176349664

Primary: 62C10
Secondary: 62A15

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 3 • September, 1985
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