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.

References

In principle, the Gaussian Ansatz should also be able to capture non-Gaussian components of the resolution. However, this has yet to be shown in a worked example.

— Unifying Simulation and Inference with Normalizing Flows  (2404.18992 - Du et al., 2024) in Section 3.3 (Resolution estimation), footnote

Whether their POVM reconstruction is subject to an analogous underestimation is not established, and cannot be ruled out.

— Single-Shot Fidelity Reveals Hard and Soft Limits: A Universal Yardstick for Photon-Number-Resolving Detectors  (2609.02503 - Tsuruta et al., 2 Sep 2026) in Section “Cross-Detector Evaluation with Real Data,” subsection “Evaluation of Rising-Edge-Timing SNSPDs”