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：当复杂的贝叶斯模型表现出不可靠行为时，一个解决方案是将现有信息整合为信息先验。挑战在于先验信息通常仅适用于可观测量或某些模型导出的边缘量，而非直接与模型中的自然参数相关。我们提出一种方法，将现有先验信息（以可观测量或模型导出边缘量的引出分布形式）转化为信息联合先验。该方法基于一个超参数尚未确定的参数化先验分布类，最小化提供的引出分布与对应先验预测分布之间的差异。我们采用全局多阶段贝叶斯优化过程来定位超参数的最优值。三个示例说明了我们的方法：治愈比例生存模型（其中删失意味着可观测量先验为混合离散/连续量）、先验信息与$R^{2}$（模型导出量）相关的情形，以及非线性回归模型。