Testing the approximations described in "Asymptotic formulae for likelihood-based tests of new physics"

TL;DR

This paper evaluates the validity and robustness of asymptotic approximations for likelihood-based hypothesis testing in high energy physics, aiming to reduce computational costs while ensuring accuracy across various scenarios.

Contribution

It systematically tests the conditions under which the asymptotic formulae remain accurate, comparing them to full calculations to establish their limits and reliability.

Findings

The approximations are valid within certain parameter ranges.

Full calculations confirm the accuracy of the approximations in tested scenarios.

The study identifies scenarios where the approximations break down.

Abstract

"Asymptotic formulae for likelihood-based tests of new physics" presents a mathematical formalism for a new approximation for hypothesis testing in high energy physics. The approximations are designed to greatly reduce the computational burden for such problems. We seek to test the conditions under which the approximations described remain valid. To do so, we perform parallel calculations for a range of scenarios and compare the full calculation to the approximations to determine the limits and robustness of the approximation. We compare this approximation against values calculated with the Collie framework, which for our analysis we assume produces true values.