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Model misspecification is a long-standing enigma of the Bayesian inferenceframework as posteriors tend to get overly concentrated on ill-informedparameter values towards the large sample limit. Tempering of the likelihoodhas been established as a safer way to do updates from prior to posterior inthe presence of model misspecification. At one extreme tempering can ignore thedata altogether and at the other extreme it provides the standard Bayes' updatewhen no misspecification is assumed to be present. However, it is an open issuehow to best recognize misspecification and choose a suitable level of temperingwithout access to the true generating model. Here we show how probabilisticclassifiers can be employed to resolve this issue. By training a probabilisticclassifier to discriminate between simulated and observed data provides anestimate of the ratio between the model likelihood and the likelihood of thedata under the unobserved true generative process, within the discriminatoryabilities of the classifier. The expectation of the logarithm of a ratio withrespect to the data generating process gives an estimation of the negativeKullback-Leibler divergence between the statistical generative model and thetrue generative distribution. Using a set of canonical examples we show thatthis divergence provides a useful misspecification diagnostic, a modelcomparison tool, and a method to inform a generalised Bayesian update in thepresence of misspecification for likelihood-based models.

Diagnosing model misspecification and performing generalized Bayes' updates via probabilistic classifiers