🤖 AI Summary
In Bayesian modeling, expert priors are often specified directly on observable or derived quantities (e.g., survival rates, R²), yet translating such domain knowledge into informative priors for latent model parameters remains a fundamental challenge.
Method: We propose a hyperparameter optimization framework grounded in prior predictive distribution matching. It parameterizes a prior family and employs multi-stage Bayesian global optimization to minimize the discrepancy between the induced prior predictive distribution and the target expert-specified distribution—supporting mixed-type and nonstandard targets, as well as censored data, nonlinear structures, and complex derived statistics.
Contribution/Results: Across three case studies—cure-rate survival models, R²-driven modeling, and nonlinear regression—the resulting informative priors substantially improve posterior stability and interpretability. Our approach provides the first systematic, computationally tractable, and empirically verifiable methodology for transforming marginal expert beliefs about observables into joint priors over latent parameters.
📝 Abstract
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 (usually latent) 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.