Empirically estimating the distribution of the loudest candidate from a gravitational-wave search

TL;DR

This paper introduces a novel method using extreme value theory to accurately estimate the distribution of the loudest detection statistic in gravitational-wave searches, accounting for template correlations and applicable to various statistics.

Contribution

It presents a new approach that generalizes to different detection statistics and improves estimation accuracy with minimal computational cost.

Findings

Effective in simulated data

Applied successfully to LIGO O2 data

Compatible with multiple detection statistics

Abstract

Searches for gravitational-wave signals are often based on maximizing a detection statistic over a bank of waveform templates, covering a given parameter space with a variable level of correlation. Results are often evaluated using a noise-hypothesis test, where the background is characterized by the sampling distribution of the loudest template. In the context of continuous gravitational-wave searches, properly describing said distribution is an open problem: current approaches focus on a particular detection statistic and neglect template-bank correlations. We introduce a new approach using extreme value theory to describe the distribution of the loudest template's detection statistic in an arbitrary template bank. Our new proposal automatically generalizes to a wider class of detection statistics, including (but not limited to) line-robust statistics and transient continuous-wave signal hypotheses, and improves the estimation of the expected maximum detection statistic at a negligible computing cost. The performance of our proposal is demonstrated on simulated data as well as by applying it to different kinds of (transient) continuous-wave searches using O2 Advanced LIGO data. We release an accompanying Python software package, distromax, implementing our new developments.