Characterization of Externally Bayesian Pooling Operators

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...

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Bibliographic Details
Published in:The Annals of statistics 1986-06, Vol.14 (2), p.487-501
Main Authors: Genest, Christian, McConway, Kevin J., Schervish, Mark J.
Format: Article
Language:English
Subjects:
39B40
62A99
Atoms
Bayes theorem
Consensus
Decision theory
Equivalence relation
Exact sciences and technology
expert opinions
external Bayesianity
logarithmic pool
Mathematical constants
Mathematical vectors
Mathematics
Probability and statistics
Probability distributions
Sciences and techniques of general use
Statistical theories
Statistics
Urelements
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176349934