Propagate w_i f_i ensemble uncertainties through neural ratio estimation to κ inference

Develop a principled method to propagate the uncertainties from w_i f_i ensemble-based neural ratio estimation into the final inference of the signal fraction κ within the exponential Template-Adapted Mixture Model (TAMM) frequentist pipeline, quantifying their impact on point estimates, confidence intervals, and coverage properties.

Background

The paper employs neural ratio estimation (NRE) to learn density ratios between misspecified simulated distributions and a reference distribution, stabilizing the estimates using w_i f_i ensembles. While these ensembles can both stabilize ratio estimates and quantify their uncertainties, the current study uses them only for stabilization and does not propagate their uncertainties into the final parameter inference.

Because the proposed exponential TAMM fits the signal fraction κ jointly with signal and background shapes using an M-estimation framework, accurately propagating uncertainties from the ratio estimators is necessary to ensure reliable confidence intervals and correct coverage, especially when simulation statistics are not overwhelmingly larger than target data.