This article describes an approach to incorporate expert opinion on observable quantities through the use of a loss function which updates a prior belief as opposed to specifying parameters on the priors. Eliciting information on observable quantities allows experts to provide meaningful information on a quantity familiar to them, in contrast to elicitation on model parameters, which may be subject to interactions with other parameters or non-linear transformations before obtaining an observable quantity. The approach to incorporating expert opinion described in this paper is distinctive in that we do not specify a prior to match an expert's opinion on observed quantity, rather we obtain a posterior by updating the model parameters through a loss function. This loss function contains the observable quantity, expressed a function of the parameters, and is related to the expert's opinion which is typically operationalized as a statistical distribution. Parameters which generate observable quantities which are further from the expert's opinion incur a higher loss, allowing for the model parameters to be estimated based on their fidelity to both the data and expert opinion, with the relative strength determined by the number of observations and precision of the elicited belief. Including expert opinion in this fashion allows for a flexible specification of the opinion and in many situations is straightforward to implement with commonly used probabilistic programming software. We highlight this using three worked examples of varying model complexity including survival models, a multivariate normal distribution and a regression problem.

翻译：本文描述了一种通过损失函数将专家对可观测量的意见纳入统计模型的方法，该损失函数用于更新先验信念，而非指定先验分布上的参数。与针对模型参数进行启发（这可能在获取可观测量前涉及参数间的交互或非线性变换）不同，针对可观测量的信息启发使专家能够就其所熟悉的量提供有意义的见解。本文所述纳入专家意见的方法独特之处在于：我们并非设定先验以匹配专家对观测量的意见，而是通过损失函数更新模型参数以获得后验分布。该损失函数包含以参数函数形式表达的可观测量，并与通常以统计分布形式操作化的专家意见相关联。生成与专家意见偏差较大的可观测量的参数将承受更高损失，从而使模型参数能够基于其对数据和专家意见的忠实度进行估计，其相对强度由观测数量及启发信念的精度决定。以这种方式纳入专家意见可灵活设定意见形式，且在多数情况下易于通过常用概率编程软件实现。我们通过三个不同复杂程度的模型实例（包括生存模型、多元正态分布及回归问题）对此加以说明。