Numerical Computation of p-values with myFitter

TL;DR

This paper introduces numerical methods for accurately computing p-values in likelihood ratio tests, applicable to both nested and non-nested models, implemented in the myFitter framework for particle physics analyses.

Contribution

It presents novel numerical techniques for p-value computation that do not depend on Wilks' theorem, suitable for complex models in particle physics.

Findings

Methods implemented in myFitter enable efficient p-value calculations.

Applied to Standard Model with a fourth fermion generation.

No reliance on Wilks' theorem for non-nested models.

Abstract

Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are, however, many realistic situations where Wilks' theorem does not apply. In particular, no simple formula exists for the comparison of models that are not nested, in the sense that one model can be obtained from the other by fixing some of its parameters. In this paper I present methods for efficient numerical computations of p-values, which work for both nested and non-nested models and do not rely on additional approximations. These methods have been implemented in a publicly available C++ framework for maximum likelihood fits called myFitter and have recently been applied in a global analysis of the Standard Model with a fourth generation of fermions.