  Driven by steady progress in generative modeling, simulation-based inference
(SBI) has enabled inference over stochastic simulators. However, recent work
has demonstrated that model misspecification can harm SBI's reliability. This
work introduces robust posterior estimation (ROPE), a framework that overcomes
model misspecification with a small real-world calibration set of ground truth
parameter measurements. We formalize the misspecification gap as the solution
of an optimal transport problem between learned representations of real-world
and simulated observations. Assuming the prior distribution over the parameters
of interest is known and well-specified, our method offers a controllable
balance between calibrated uncertainty and informative inference under all
possible misspecifications of the simulator. Our empirical results on four
synthetic tasks and two real-world problems demonstrate that ROPE outperforms
baselines and consistently returns informative and calibrated credible
intervals.
