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

TL;DR

This paper introduces an efficient linear approximation method to estimate the covariance matrix of Gaussian fields in high-energy physics significance scans, enabling better calculation of trials factors in particle searches.

Contribution

The paper presents a novel linear approximation approach to estimate the covariance matrix, improving efficiency in significance analysis for high-energy physics experiments.

Findings

Efficient covariance matrix estimation for Gaussian fields

Direct calculation of trials factors in 1D searches

Sampling-based trials factor estimation in higher dimensions

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 $H \rightarrow \gamma \gamma$ inspired model that was used in the empirical paper.