Generative Bayesian Modeling with Implicit Priors

Generative models are a cornerstone of Bayesian data analysis, enabling predictive simulations and model validation. However, in practice, manually specified priors often lead to unreasonable simulation outcomes, a common obstacle for full Bayesian simulations. As a remedy, we propose to add small portions of real or simulated data, which creates implicit priors that improve the stability of Bayesian simulations. We formalize this approach, providing a detailed process for constructing implicit priors and relating them to existing research in this area. We also integrate the implicit priors into simulation-based calibration, a prominent Bayesian simulation task. Through two case studies, we demonstrate that implicit priors quickly improve simulation stability and model calibration. Our findings provide practical guidelines for implementing implicit priors in various Bayesian modeling scenarios, showcasing their ability to generate more reliable simulation outcomes.