Calibrated Model Criticism Using Split Predictive Checks

Checking how well a fitted model explains the data is one of the most fundamental parts of a Bayesian data analysis. However, existing model checking methods suffer from trade-offs between being well-calibrated, automated, and computationally efficient. To overcome these limitations, we propose split predictive checks (SPCs), which combine the ease-of-use and speed of posterior predictive checks with the good calibration properties of predictive checks that rely on model-specific derivations or inference schemes. We develop an asymptotic theory for two types of SPCs: single SPCs and the divided SPC. Our results demonstrate that they offer complementary strengths: single SPCs provide superior power in the small-data regime or when the misspecification is significant and divided SPCs provide superior power as the dataset size increases or when the form of misspecification is more subtle. We validate the finite-sample utility of SPCs through extensive simulation experiments in exponential family and hierarchical models, and provide four real-data examples where SPCs offer novel insights and additional flexibility beyond what is available when using posterior predictive checks.