arXiv subjects

A. L. Read

Publications and source records attributed to A. L. Read.

3 recordsLinked to original sources

arXiv2025

The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments

Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks' theorem. This assumption breaks down when parameters such as signal or coupling strengths are restricted to be non-negative and their values under the null hypothesis lie on the boundary of the parameter space. Based on a recent clarification concerning the correct asymptotic distribution of the likelihood ratio test statistic for cases where two of the parameters are on the boundary, we revisit the the question of significance estimation for two-peak signal-plus-background counting experiments. In the high-energy physics literature, such experiments are commonly analyzed using Wilks' chi-squared distribution or the one-parameter Chernoff limit. We demonstrate that these approaches can lead to strongly miscalibrated significances, and that the test statistic distribution is instead well described by a chi-squared mixture with weights determined by the Fisher information matrix. Our results highlight the need for boundary-aware asymptotics in the analysis of two-peak counting experiments.

hep-ex↗

arXiv2023

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

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.

physics.data-an↗

arXiv2022

Gaussian Process-based calculation of look-elsewhere trials factor

In high-energy physics it is a recurring challenge to efficiently and precisely (enough) calculate the global significance of, e.g., a potential new resonance. We propose a new method that models the significance in the search region as a Gaussian Process. The kernel of the Gaussian Process is approximated with a covariance matrix and is calculated with a carefully designed set of background-only data sets, comparable in number to the random background-only data sets used in a typical analysis that relies on the average upcrossings of the significance. The trials factor for both low and moderate significances can subsequently be calculated to the desired precision with a computationally inexpensive random sampling of the Gaussian Process. In addition, once the covariance of the Gaussian Process is determined, the average number of upcrossings can be computed analytically. In our work we give some highlights of the analytic calculation and also discuss some peculiarities of the trials factor estimation on a finite grid. We illustrate the method with studies of three complementary statistical models.

stat.ME↗