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Mathematical models are an important tool to explain and comprehend complex phenomena, and unparalleled computational advances enable us to easily explore them without any or little understanding of their global properties. In fact, the likelihood of the data under complex stochastic models is often analytically or numerically intractable in many areas of sciences. This makes it even more important to simultaneously investigate the adequacy of these models—in absolute terms, against the data, rather than relative to the performance of other models—but no such procedure has been formally discussed when the likelihood is intractable. We provide a statistical interpretation to current developments in likelihood-free Bayesian inference that explicitly accounts for discrepancies between the model and the data, termed Approximate Bayesian Computation under model uncertainty (ABCμ). We augment the …