Multiple Probability Assessments by Dependent Experts
研究了当多个专家提供多个随机变量的概率评估时，决策者如何利用贝叶斯规则同时更新先验和校准专家，并给出了评估误差服从多元正态分布时的后验密度公式。
Abstract When two or more information sources ("experts") provide a decision maker with information on two or more random variables, the decision maker using Bayes's rule has an opportunity to (a) update a prior about the random variables and (b) calibrate the experts. (Calibration is the process of adjusting the decision maker's likelihood about the experts' assessments.) This article presents a model for this two-way process and specializes to the case in which the experts' assessment errors have a multivariate normal density. In general, we find that variables which the decision maker and the experts regard as independent a priori will be dependent a posteriori because of dependence in the assessment errors. Formulas for posterior densities are given for the normal model. In this model the posterior density of the random variables depends on only a weighted average of the expert's means, with weights that depend on the experts' assessments of previously known quantities. I also present a special case of the model for which the mean of the posterior density is correctly given by a simple (unweighted) average of assessments.