A study of convex hull optimization and null-stream-based chi squared discrimination statistics for gravitational-wave signal analysis
Dupree, William Zachary
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We develop data analysis methods to improve the sensitivity of searches for gravitational-wave signals from compact object binaries in networks of ground-based detectors, such as LIGO, Virgo and KAGRA. These are targeted for two different aspects of gravitational-wave data analysis. One focuses on blind searches in the sky, while the other improves the ability to veto triggers arising from spurious noise in detectors. The convex hull optimization focuses on maximizing the search statistic over the sky location parameters. This is done by bounding the search statistic by a convex function. This allows an all-sky search to effectively become a search over the convex set of detector data in the time delay parameter. We cut down on needed operations by searching the boundary (termed its convex hull) of this set of points, effectively searching over a smaller parameter space. We give the efficiency of such an algorithmic approach by comparing number of compute operations done to search the sky between current methods and our convex hull method. Our simulations show a gain in efficiency by a factor of seven or more, depending on the detector network used to perform a sky search. We also develop a veto for discriminating noise transients from compact binary coalescence signals. In some cases noise transients known as glitches match a signal search template well enough to generate a false trigger. We develop a network based statistic that distinguishes between gravitational-wave signal and noise triggers. This is done by combining a well known Chi-Squared statistic for single detectors with a null stream constructed veto for networks of detectors. The null stream is a linear combination of detector data constructed to remove any gravitational-wave signal content from it, leaving only detector noise. We then use this construction to compare data to signal template over smaller frequency windows in the detector band. Doing so allows for a more accurate test on how well a template matches over a given frequency range. Using simulated data, we show support for our null stream based statistic to perform as well, or better, than previous vetoing methods.