A Frequentist Simulation-Based Inference Treatment of Sterile Neutrino Global Fits

TL;DR

This paper introduces a simulation-based inference method to perform frequentist global fits of sterile neutrino data, overcoming computational challenges and relaxing Wilks' theorem assumptions, enabling more robust and efficient analyses.

Contribution

It presents a novel SBI-based approach for frequentist inference in complex likelihood scenarios, significantly reducing computation and incorporating systematic uncertainties.

Findings

Speeded up likelihood ratio estimation by over 10,000 times per grid point.

Enabled the first global sterile neutrino fit without relying on Wilks' theorem.

Demonstrated robustness and efficiency in analyzing muon-flavor neutrino disappearance data.

Abstract

A critical challenge in particle physics is combining results from diverse experimental setups that measure the same physical quantity to enhance precision and statistical power, a process known as a global fit. Global fits of sterile neutrino searches, hunts for additional neutrino oscillation frequencies and amplitudes, present an intriguing case study. In such a scenario, the key assumptions underlying Wilks' theorem, a cornerstone of most classic frequentist analyses, do not hold. The method of Feldman and Cousins, a trials-based approach which does not assume Wilks' theorem, becomes computationally prohibitive for complex or intractable likelihoods. To bypass this limitation, we borrow a technique from simulation-based inference (SBI) to estimate likelihood ratios for use in building trials-based confidence intervals, speeding up test statistic evaluations by a factor $>10^4$ per grid point, resulting in a faster, but approximate, frequentist fitting framework. Applied to a subset of sterile neutrino search data involving the disappearance of muon-flavor (anti)neutrinos, our method leverages machine learning to compute frequentist confidence intervals while significantly reducing computational expense. In addition, the SBI-based approach holds additional value by recognizing underlying systematic uncertainties that the Wilks approach does not. Thus, our method allows for more robust machine learning-based analyses critical to performing accurate but computationally feasible global fits. This allows, for the first time, a global fit to sterile neutrino data without assuming Wilks' theorem. While we demonstrate the utility of such a technique studying sterile neutrino searches, it is applicable to both single-experiment and global fits of all kinds.