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) continuouswave searches using O2 Advanced LIGO data. We release an accompanying PYTHON software package, distromax, implementing our new developments.

Narrowband searches for continuous and long-duration transient gravitational waves from known pulsars in the LIGO-Virgo third observing run

“…To determine whether or not there are interesting outliers in the results of each search, for most targets we again follow the procedure described in Tenorio et al (2021c) to empirically estimate the distribution of the expected highest outlier. For two targets, PSR J1105-6107 and PSR J1826-1334, the number of templates is too low for this method to deliver robust results.…”

“…Following Tenorio et al (2021c), we construct 10 4 randomly-chosen batches of templates from our search results for each pulsar, and fit a Gumbel distribution to the distribution of the maxima of these batches. We can then propagate this Gumbel distribution based on the total number of templates to estimate the tail probability (p-value) of the largest template across the full search for that target.…”

“…We then set a threshold corresponding to a p-value of 1% under the assumption that no signal is present in the data. We use the distromax method introduced by Tenorio et al (2021c), with some slight modifications due to the specific situation at hand.…”

“…4. Perform a single iteration of the notching procedure from Tenorio et al (2021c), which removes templates with a frequency within 5 × 10 −5 Hz of any template exceeding an internal threshold.…”

“…6. Propagate that Gumbel distribution based on the number of batches (Tenorio et al 2021c), and the total number of templates (i.e., the number of templates used before we perform notching, since this is the number of templates used to perform the search) to obtain a distribution for the maximum of the full search for that individual pulsar.…”