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

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.

arXiv comment24 pages, 23 figures, comments welcome. Package freely available in https://github.com/Rodrigo-Tenorio/distromax

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