Gravitational-Wave Geodesy: Defining False Alarm Probabilities with Respect to Correlated Noise

TL;DR

This paper formalizes a method called gravitational-wave geodesy to differentiate true gravitational-wave background signals from terrestrial noise, using Bayesian analysis and Gaussian processes to quantify false alarm probabilities.

Contribution

It introduces a formal framework mapping false-alarm and false-acceptance probabilities for gravitational-wave geodesy, enhancing detection confidence assessment.

Findings

Mapped false-alarm probabilities to Bayes factors.

Constructed Gaussian process models for terrestrial noise.

Applied method to LIGO/Virgo data with SNR=1.25.

Abstract

Future searches for a gravitational-wave background using Earth-based gravitational-wave detectors might be impacted by correlated noise sources. A well known example are the Schumann resonances, which are extensively studied in the context of searches for a gravitational-wave background. Earlier work has shown that a technique termed "gravitational-wave geodesy" can be used to generically differentiate observations of a gravitational-wave background from signals due to correlated terrestrial effects, requiring true observations to be consistent with the known geometry of our detector network. The key result of this test is a Bayes factor between the hypotheses that a candidate signal is astrophysical or terrestrial in origin. Here, we further formalize the geodesy test, mapping distributions of false-alarm and false-acceptance probabilities to quantify the degree with which a given Bayes factor will boost or diminish our confidence in an apparent detection of the gravitational-wave background. To define the false alarm probability of a given Bayes factor, we must have knowledge of our null hypothesis: the space of all possible correlated terrestrial signals. Since we do not have this knowledge we instead construct a generic space of smooth functions in the frequency domain using Gaussian processes, which we tailor to be conservative. This enables us to use draws from our Gaussian processes as a proxy for all possible non-astrophysical signals. As a demonstration, we apply the tool to the SNR = 1.25 excess observed for a 2/3-power law by the LIGO and Virgo collaborations during their second observing run.