Bayesian model criticism using uniform parametrization checks

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.