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Simulator-based models are models for which the likelihood is intractable butsimulation of synthetic data is possible. They are often used to describecomplex real-world phenomena, and as such can often be misspecified inpractice. Unfortunately, existing Bayesian approaches for simulators are knownto perform poorly in those cases. In this paper, we propose a novel algorithmbased on the posterior bootstrap and maximum mean discrepancy estimators. Thisleads to a highly-parallelisable Bayesian inference algorithm with strongrobustness properties. This is demonstrated through an in-depth theoreticalstudy which includes generalisation bounds and proofs of frequentistconsistency and robustness of our posterior. The approach is then assessed on arange of examples including a g-and-k distribution and a toggle-switch model.

Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap