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:本条介绍了一种方法,通过使用更新先前信念而不是具体说明前期参数的损失功能,纳入关于可观察数量的专家意见; 关于可观察数量的信息,使专家能够就他们熟悉的数量提供有意义的信息,而与模型参数的引证相反,模型参数可能与其他参数或非线性变异发生相互作用,然后才能获得可观察数量; 本文所述纳入专家意见的方法有其独特之处,因为我们没有事先具体规定与专家关于已观察数量的意见相匹配,而是通过损失函数更新模型参数取得后遗体。 这一损失函数包含可观察数量,表示参数的功能,与专家意见有关,通常作为一种统计分布方式运作。 产生可观察数量的参数,从专家意见中进一步得出,则造成更高的损失,使得模型参数能够根据它们对数据和专家意见的忠实性来估计,而模型的相对强度则由观察数量和所了解的信念的精确性确定。 包括专家意见的相对强度,这种形式中包含观察到的数量,表示参数的功能,与专家意见有关,通常作为统计分布方式运作的专家意见有关。