Gravitational-wave geodesy: Defining false alarm probabilities with respect to correlated noise
(2022) Physical review D — Vol. 105 (2022)
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., Jishnu Suresh 
- et. al.
- 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 nonastrophysical signals. During the O2 observing run, the LIGO and Virgo collaborations observed an <math display="inline"><mrow><mi>SNR</mi><mo>=</mo><mn>1.25</mn></mrow></math> excess in their search for an isotropic gravitational-wave background. To demonstrate the utility of gravitational-wave geodesy, we apply the method to the observed cross-correlated data.
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Janssens, K., others, ., J. S., & et al. (2022). Gravitational-wave geodesy: Defining false alarm probabilities with respect to correlated noise. Physical review D, 105. https://doi.org/10.1103/PhysRevD.105.082001 (Original work published 2022)