Combining Probability Distributions from Dependent Information Sources

Abstract

Inferences or decisions in the face of uncertainty should be based on all available information. Thus, when probability distributions for an uncertain quantity are obtained from experts, models, or other information sources, these distributions should be combined to form a single consensus distribution upon which inferences and decisions can be based. An important feature of information from different sources is the possibility of stochastic dependence, and a consensus model which formally allows for such dependence is developed in this paper. Under normality, the model yields reasonably tractable results, and the consensus distribution is quite sensitive to the degree of dependence.