When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the natural parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimises the difference between the supplied elicited distribution and corresponding prior predictive distribution. We employ a global, multi-stage Bayesian optimisation procedure to locate optimal values for the hyperparameters. Three examples illustrate our approach: a cure-fraction survival model, where censoring implies that the observable quantity is a priori a mixed discrete/continuous quantity; a setting in which prior information pertains to $R^{2}$ -- a model-derived quantity; and a nonlinear regression model.

翻译：当复杂贝叶斯模型表现出不合理行为时，一种解决方案是将现有信息整合为信息性先验。然而，由于先验信息通常仅针对可观测量或模型推导的边缘量，而非直接对应模型中的自然参数，这带来了挑战。我们提出了一种方法，可将以可观测量或模型推导的边缘量的引出分布形式存在的现有先验信息，转化为信息性联合先验。该方法基于超参数尚未确定的参数化先验分布族，最小化提供的引出分布与相应的先验预测分布之间的差异。我们采用全局、多阶段的贝叶斯优化过程来确定超参数的最优值。三个示例说明了我们的方法：一个治愈分数生存模型（其中删失意味着可观测量先验上是混合离散/连续量）；一个先验信息涉及$R^{2}$（模型推导量）的场景；以及一个非线性回归模型。