Modeling Expert Opinion Arising as a Partial Probabilistic Specification
针对单变量未知量，将专家以区间概率或分位数形式给出的部分概率意见视为数据，通过贝叶斯定理合成决策者自身意见，得到后验分布作为意见池化结果，并应用于1991年NBA总决赛球员场均得分预测。
Abstract Expert opinion is often sought with regard to unknowns in a decision-making setting. For a univariate unknown, θ, our presumption is that such opinion is elicited as a partial probabilistic specification in the form of either probability assignments regarding the chance of θ falling in a fixed set of disjoint exhaustive intervals or selected quantiles for θ. Treating such specification as “data,” our focus is on the development of suitable probability densities for these data given the true θ. In particular, we advocate a rich class of densities created by transformation of random mixtures of beta distributions. These densities become likelihoods when viewed as a function of θ given the data. We presume that a decision-maker (here a so-called supra Bayesian) presides over the opinion collection, offering his or her assessment as well. All of this opinion is synthesized using Bayes's theorem, resulting in the posterior distribution as the pooling mechanism. The models are applied to opinion collected regarding points per game for participants in the 1991 National Basketball Association championship basketball series.