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 SPCs. Our results demonstrate that they offer complementary strengths. Single SPCs work well with smaller datasets and provide excellent power when there is substantial misspecification, such as when the estimate uncertainty in the test statistic is significantly underestimated. When the sample size is large, divided SPCs can provide better power and are able to detect more subtle form of misspecification. We validate the finite-sample utility of SPCs through extensive simulation experiments in exponential family and hierarchical models, and provide three real-data examples where SPCs offer novel insights and additional flexibility beyond what is available when using posterior predictive checks.