We consider the problem of aggregating the judgements of a group of experts to form a single prior distribution representing the judgements of the group. We develop a Bayesian hierarchical model to reconcile the judgements of the group of experts based on elicited quantiles for continuous quantities and probabilities for one-off events. Previous Bayesian reconciliation methods have not been used widely, if at all, in contrast to pooling methods and consensus-based approaches. To address this we embed Bayesian reconciliation within the probabilistic Delphi method. The result is to furnish the outcome of the probabilistic Delphi method with a direct probabilistic interpretation, with the resulting prior representing the judgements of the decision maker. We can use the rationales from the Delphi process to group the experts for the hierarchical modelling. We illustrate the approach with applications to studies evaluating erosion in embankment dams and pump failures in a water pumping station, and assess the properties of the approach using the TU Delft database of expert judgement studies. We see that, even using an off-the-shelf implementation of the approach, it out-performs individual experts, equal weighting of experts and the classical method based on the log score.

翻译：我们考虑如何汇总一组专家的判断，以形成代表该组判断的单一先验分布。我们开发了一个贝叶斯分层模型，基于对连续量的分位数和一次性事件概率的启发式推断，来调和专家组判断。以往的贝叶斯调和法（如有应用）尚未广泛采用，这与池化法和基于共识的方法形成对比。为解决此问题，我们将贝叶斯调和嵌入概率型德尔菲法中。其结果是为概率型德尔菲法的输出提供直接的概率解释，使得最终先验分布代表决策者的判断。我们可以利用德尔菲过程中的论据，将专家分组用于分层建模。我们通过评估堤坝侵蚀和水泵站泵体故障的研究案例来演示该方法，并利用代尔夫特理工大学专家判断研究数据库评估该方法的特性。我们发现，即使采用现成的实现方式，该方法也优于单个专家、等权重专家组合以及基于对数得分法的经典方法。