  Recent advances in probabilistic deep learning enable efficient amortized
Bayesian inference in settings where the likelihood function is only implicitly
defined by a simulation program (simulation-based inference; SBI). But how
faithful is such inference if the simulation represents reality somewhat
inaccurately, that is, if the true system behavior at test time deviates from
the one seen during training? We conceptualize the types of such model
misspecification arising in SBI and systematically investigate how the
performance of neural posterior approximators gradually deteriorates as a
consequence, making inference results less and less trustworthy. To notify
users about this problem, we propose a new misspecification measure that can be
trained in an unsupervised fashion (i.e., without training data from the true
distribution) and reliably detects model misspecification at test time. Our
experiments clearly demonstrate the utility of our new measure both on toy
examples with an analytical ground-truth and on representative scientific tasks
in cell biology, cognitive decision making, disease outbreak dynamics, and
computer vision. We show how the proposed misspecification test warns users
about suspicious outputs, raises an alarm when predictions are not trustworthy,
and guides model designers in their search for better simulators.
