When precision exceeds fidelity: systematic error quantification for inference with misspecified simulators

As scientific datasets grow in complexity and precision, the primary source of uncertainty in parameter inference shifts from measurement noise to systematic errors within the simulators themselves. In this setting, Bayesian evidence concentrates on whichever misspecified model best approximates the data, so evidence-weighted model averaging assigns no systematic uncertainty, even when one model component can compensate for the misspecification of another component and thus bias the fit. We posit that in this case, the key question is how each model responds to discrepancies between simulator and data. We show that the local response of an inferred parameter to perturbations in the data --- the model's influence map --- can be estimated efficiently from forward evaluations of the simulator at existing posterior samples. Propagating discrepancy residuals through these influence maps enables individual sources of systematic bias to be isolated. Applied to independent observations used to infer the mass of a supermassive black hole, we find that the error is dominated by model systematics. We identify a simplification shared by all models, propagate the discrepancies through each model's influence map, and apply a first-order correction of the resulting biases. This substantially improves the cross-observation consistency of the inferred black-hole mass within each model while preserving the between-model spread that represents remaining systematics.