A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior distributions over model parameters, a process known as prior elicitation. Expert knowledge can manifest itself in diverse formats, including information about raw data, summary statistics, or model parameters. A major challenge for existing elicitation methods is how to effectively utilize all of these different formats in order to formulate prior distributions that align with the expert's expectations, regardless of the model structure. To address these challenges, we develop a simulation-based elicitation method that can learn the hyperparameters of potentially any parametric prior distribution from a wide spectrum of expert knowledge using stochastic gradient descent. We validate the effectiveness and robustness of our elicitation method in four representative case studies covering linear models, generalized linear models, and hierarchical models. Our results support the claim that our method is largely independent of the underlying model structure and adaptable to various elicitation techniques, including quantile-based, moment-based, and histogram-based methods.

翻译：贝叶斯统计的核心特征之一是能够将先验知识一致地融入各种建模过程。本文重点研究将领域专家知识转化为模型参数上的相应先验分布，这一过程称为先验获取。专家知识可以表现为多种形式，包括原始数据信息、汇总统计量或模型参数信息。现有获取方法面临的主要挑战是如何有效利用所有这些不同形式的知识，以构建符合专家期望的先验分布，且不受模型结构限制。为解决这些挑战，我们提出了一种基于仿真的获取方法，该方法能够利用随机梯度下降法从广泛的专家知识中学习任意参数化先验分布的超参数。我们通过涵盖线性模型、广义线性模型和层次模型的四个代表性案例研究，验证了所提获取方法的有效性和鲁棒性。结果表明，我们的方法能基本独立于底层模型结构，并适用于多种获取技术，包括基于分位数、基于矩和基于直方图的方法。