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：贝叶斯统计的一个核心特征是在各种建模过程中能够一致地融入先验知识。本文聚焦于将领域专家知识转化为模型参数上的对应先验分布，这一过程被称为先验知识抽取。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。现有抽取方法面临的主要挑战是如何有效利用所有这些不同格式的知识，以制定符合专家期望的先验分布，无论模型结构如何。为解决这些挑战，我们开发了一种基于仿真的抽取方法，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。我们在四个代表性案例研究（涵盖线性模型、广义线性模型及层次模型）中验证了所提抽取方法的有效性和稳健性。研究结果支持以下论断：我们的方法在很大程度上独立于底层模型结构，并能适应包括分位数法、矩法和直方图法在内的多种抽取技术。