🤖 AI Summary
This paper addresses the lack of directionality, statistical rigor, and computational efficiency in Bayesian model misspecification diagnostics. We propose a novel diagnostic framework based on Uniform Parameterization Checks (UPCs). Our core innovation is the first systematic exploitation of the theoretical property that posterior samples should follow the prior distribution under correct model specification; leveraging probability integral transforms, UPCs uniformly map all random components—across prior, likelihood, and data—into independent *u*-values. This enables interpretable, aggregable, statistically rigorous, and computationally efficient diagnostics (≈ cost of one posterior sample) for individual model components (prior, likelihood, data subsets). UPCs support targeted detection of specific misspecification types—including dependence structure violations, tail discrepancies, and missing correlations—and accurately localize sources of misspecification in both synthetic and real-world examples. Theoretical analysis establishes consistency of the proposed tests.
📝 Abstract
Models are often misspecified in practice, making model criticism a key part of Bayesian analysis. It is important to detect not only when a model is wrong, but which aspects are wrong, and to do so in a computationally convenient and statistically rigorous way. We introduce a novel method for model criticism based on the fact that if the parameters are drawn from the prior, and the dataset is generated according to the assumed likelihood, then a sample from the posterior will be distributed according to the prior. Thus, departures from the assumed likelihood or prior can be detected by testing whether a posterior sample could plausibly have been generated by the prior. Building upon this idea, we propose to reparametrize all random elements of the likelihood and prior in terms of independent uniform random variables, or u-values. This makes it possible to aggregate across arbitrary subsets of the u-values for data points and parameters to test for model departures using classical hypothesis tests for dependence or non-uniformity. We demonstrate empirically how this method of uniform parametrization checks (UPCs) facilitates model criticism in several examples, and we develop supporting theoretical results.