Linear approximation to the statistical significance autocovariance matrix in the asymptotic regime

Abstract

Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel, highly efficient method to estimate the covariance matrix of such a Gaussian field. The method is based on the linear approximation of statistical fluctuations of the signal amplitude. For one-dimensional searches the upper bound on the trials factor can then be calculated directly from the covariance matrix. For higher dimensions, the Gaussian process described by this covariance matrix may be sampled to calculate the trials factor directly. This method also serves as the theoretical basis for a recent study of the trials factor with an empirically constructed set of Asmiov-like background datasets. We illustrate the method with studies of a $H\to \gamma \gamma$ inspired model that was used in the empirical paper.

arXiv comment9 pages, 2 figures

References in corpus (6)

• Asymptotic formulae for likelihood-based tests of new physics
• Trial factors for the look elsewhere effect in high energy physics
• Search for the Standard Model Higgs boson in the diphoton decay channel with 4.9 fb-1 of pp collisions at sqrt(s) = 7 TeV with ATLAS
• Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV
• Estimating the significance of a signal in a multi-dimensional search
• Gaussian Process-based calculation of look-elsewhere trials factor