Demonstrating non-Gaussian resolution capture with the Gaussian Ansatz

Demonstrate in a worked example whether the Gaussian Ansatz approach to maximum likelihood calibration can capture non-Gaussian components of the per-event resolution function in detector calibration, by constructing and validating an explicit example beyond purely Gaussian resolutions.

Background

The authors emphasize that access to the full likelihood with normalizing flows enables characterization of non-Gaussian resolution features, including asymmetries. They remark that, in principle, the Gaussian Ansatz could also capture non-Gaussian components, but this capability has not been shown in practice.

Establishing such a worked example would clarify the generality of the Gaussian Ansatz for uncertainty modeling in calibration tasks and provide a direct comparison to normalizing flows for non-Gaussian resolution characterization.