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

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.

arXiv comment22 pages, 6 figures, match the journal version

References in corpus (7)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Asymptotic formulae for likelihood-based tests of new physics
• Measurements of Higgs boson properties in the diphoton decay channel with 36 fb${}^{-1}$ of $pp$ collision data at $\sqrt{s}=13$ TeV with the ATLAS detector
• Search for doubly charged scalar bosons decaying into same-sign $W$ boson pairs with the ATLAS detector
• Measurement of the $Z\gamma \to \nu \bar{\nu }\gamma$ production cross section in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector and limits on anomalous triple gauge-boson couplings
• Evidence for the associated production of a single top quark and a photon in proton-proton collisions at $\sqrt{s}=$ 13 TeV

Cited by in corpus (3)

• The $Higgs\to b\bar{b},c\bar{c},gg$ measurement at CEPC
• Probing $\Delta L=2$ lepton number violating SMEFT operators at the same-sign muon collider
• Improved Asymptotic Formulae for Statistical Interpretation Based on Likelihood Ratio Tests