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Checking how well a fitted model explains the data is one of the mostfundamental parts of a Bayesian data analysis. However, existing model checkingmethods suffer from trade-offs between being well-calibrated, automated, andcomputationally efficient. To overcome these limitations, we propose splitpredictive checks (SPCs), which combine the ease-of-use and speed of posteriorpredictive checks with the good calibration properties of predictive checksthat rely on model-specific derivations or inference schemes. We develop anasymptotic theory for two types of SPCs: single SPCs and the divided SPC. Ourresults demonstrate that they offer complementary strengths: single SPCsprovide superior power in the small-data regime or when the misspecification issignificant and divided SPCs provide superior power as the dataset sizeincreases or when the form of misspecification is more subtle. We validate thefinite-sample utility of SPCs through extensive simulation experiments inexponential family and hierarchical models, and provide four real-data exampleswhere SPCs offer novel insights and additional flexibility beyond what isavailable when using posterior predictive checks.

Calibrated Model Criticism Using Split Predictive Checks