Pooling Expert Opinions on Probability Distributions

Abstract

When several probability distributions are to be synthesized into one, there are certain consistency requirements that generally should be satisfied. They include symmetry, continuity, conservation of form, Bayesian coherence, and application consistency. A vector space formulation of Bayes' theorem is used to derive a convenient restatement of Bayesian coherence. It is shown that a logarithmic pooling formula satisfies the requirements of Bayesian coherence, symmetry, and continuity. It is possible to satisfy the requirements of application consistency in some specific contexts; this is illustrated by an example drawn from highway bridge loads.