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

In this paper, 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 detection statistic. Based on the estimated $p$-values, we propose a procedure to assess the significance of a particular event with the false discovery rate. The false discovery rate can distinguish gravitational wave events from noise events and can give us a different criterion of a significance from the conventional method. The proposed procedure is demonstrated by reanalyzing the results of the analysis of the first observing run (O1) data of advanced LIGO. As a result, we find that GW150914, GW151226, and GW151012 should be called significant, if the events whose false discovery rate is smaller than 0.05 are called significant. The result is consistent with the recent catalog of gravitational waves from compact binary coalescences. In addition, the result shows that the procedure presented in this paper has advantages over powerful than the method controlling the $P_{\rm astro}$, which is a conventional measure of the false discovery rate. The proposed procedure is applicable to other searches for gravitational waves whose background distribution of detection statistic is difficult to know.