A nonparametric method to assess the significance of events in the search for gravitational waves with false discovery rate

Abstract

Abstract We present a consistent procedure to assess the significance of gravitational wave events observed by laser interferometric gravitational wave detectors based on the background distribution of the detection statistic. We propose a non-parametric method to estimate the p-value. Based on the estimated p-values, we propose a new procedure to assess the significance of a particular event with a q-value which is the minimum false discovery rate that can be attained when calling the event significant. The q-value gives us a criterion on the significance of events which is different from Pastro as used in the LIGO–Virgo analysis and others. The proposed procedure is applied to the 1-OGC and 2-OGC catalogs. For most of the events which were claimed significant in these catalogs, we obtain the same results. However, there are differences in the significance for several marginal events. Since the proposed procedure does not require any assumptions on signal and noise, it is very simple and straightforward. The procedure is also applicable to other searches for gravitational waves whose background distribution of the detection statistic is difficult to know.