Study of constraint and impact of a nuisance parameter in maximum likelihood method

TL;DR

This paper investigates the constraints and impacts of nuisance parameters in maximum likelihood estimations, providing simple formulas to understand and estimate these effects efficiently in high energy physics analyses.

Contribution

It introduces analytical formulas to estimate the constraint and impact of nuisance parameters, simplifying the analysis of complex likelihood fits with many parameters.

Findings

Derived formulas for constraint estimation

Formulas for impact assessment

Enhanced understanding of nuisance parameter effects

Abstract

Maximum likelihood method is widely used for parameter estimation in high energy physics. To consider various systematic uncertainties, tens of or even hundreds of nuisance parameters (NP) are introduced in a likelihood fit. The constraint of a nuisance parameter and its impact on the parameter of interest (POI) will be the main concerns for a precise measurement. A fit involving many parameters is usually slow and it is even more time-consuming to investigate why a parameter is over-constrained or has a large impact. In this paper, we are trying to understand the reasons behind and provide simple formulae to estimate the constraint and impact directly.