The Annals of Statistics

Characterization of Externally Bayesian Pooling Operators

Christian Genest, Kevin J. McConway, and Mark J. Schervish

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When a panel of experts is asked to provide some advice in the form of a group probability distribution, the question arises as to whether they should synthesize their opinions before or after they learn the outcome of an experiment. If the group posterior distribution is the same whatever the order in which the pooling and the updating are done, the pooling mechanism is said to be externally Bayesian by Madansky (1964). In this paper, we characterize all externally Bayesian pooling formulas and we give conditions under which the opinion of the group will be proportional to the geometric average of the individual densities.

Article information

Ann. Statist. Volume 14, Number 2 (1986), 487-501.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A99: None of the above, but in this section
Secondary: 39B40

Consensus expert opinions external Bayesianity logarithmic pool


Genest, Christian; McConway, Kevin J.; Schervish, Mark J. Characterization of Externally Bayesian Pooling Operators. Ann. Statist. 14 (1986), no. 2, 487--501. doi:10.1214/aos/1176349934.

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