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 nonlinear regression model; a setting in which prior information pertains to $R^{2}$ -- a model-derived quantity; and a cure-fraction survival model, where censoring implies that the observable quantity is a priori a mixed discrete/continuous quantity.

翻译：当复杂贝叶斯模型出现不合理行为时，一种解决方案是将可用信息整合为有信息先验。由于先验信息通常仅针对可观测变量或模型推导的边缘量，而非直接关联模型中的自然参数，这带来了挑战。我们提出一种方法，将以可观测变量或模型推导边缘量的引出分布形式呈现的可用先验信息，转化为有信息联合先验。该方法在给定具有尚未确定超参数的参数化先验分布族的前提下，最小化提供的引出分布与对应的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程序来定位超参数的最优值。三个示例说明了我们的方法：一个非线性回归模型；一个先验信息涉及模型推导量$R^{2}$的场景；以及一个治愈分数生存模型，其中删失使得可观测变量先验上呈现混合离散/连续量的特征。