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:当复杂的贝叶斯模型表现出难以置信的行为时,一个解决办法是将现有信息汇集成一个信息丰富的先行方法。挑战出现,因为以前的信息往往只针对可观测的数量,或一些模型派生的边际数量,而不是与我们模型的自然参数直接相关。我们提出了一个方法,将已有的先行信息以可观测数量或模型派生的边际数量引出的方式转化为先见的共同信息。我们的方法是,将先前分布的参数类别与尚未确定的超分光计相匹配,并尽可能缩小所提供的已获取的分布和相应的先前预测分布之间的差异。我们采用了全球多阶段巴伊西亚优化程序来确定超分光计的最佳值。三个例子说明了我们的方法:非线回归模型;先前信息涉及$R<unk> 2美元 -- -- 模型派生量;以及治疗违约生存模型,其中审查表明,可观测数量是先知的混合离散/连续的数量。</s>