Is the bump significant? An axion-search example

TL;DR

This paper introduces a high-precision extrapolation method for the runs statistic, enabling efficient analysis of large datasets in physics experiments, demonstrated on axion search data.

Contribution

It presents a novel extrapolation technique for the runs statistic, improving computational efficiency for large datasets in physics spectrum analysis.

Findings

Method accurately extrapolates runs statistic for millions of data points.

Verified approach with benchmark cases.

Successfully applied to real axion search data.

Abstract

Many experiments in physics involve searching for a localized excess over background expectations in an observed spectrum. If the background is known and there is Gaussian noise, the amount of excess of successive observations can be quantified by the runs statistic taking care of the look-elsewhere effect. The distribution of the runs statistic under the background model is known analytically but the computation becomes too expensive for more than about a hundred observations. This work demonstrates a principled high-precision extrapolation from a few dozen up to millions of data points. It is most precise in the interesting regime when an excess is present. The method is verified for benchmark cases and successfully applied to real data from an axion search. The code that implements our method is available at https://github.com/fredRos/runs .