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

Abstract

During recent observation runs by LIGO and Virgo, tens of gravitational wave events have been observed. The gravitational wave network of LIGO/Virgo/KAGRA is planning longer observation runs with improved sensitivity in the future. In this situation, it is important to evaluate the significance of each event with reliable methods since we expect, as the observation period becomes longer and as the sensitivity of the detector improves, we expect to detect more false positive events with a given threshold for the false alarm rate. In this paper, we introduce q-value which was first introduced by Storey[1], and is interpreted as False Discovery Rate (FDR). We introduce an algorithm to evaluate FDR in a non-parametric way, and apply it to publically available results of the analysis of the advanced LIGO O1 data, and find that we can obtain a better significance for GW151012 which has the lowest significance in the O1 events. For other events, we obtain consistent results already obtained by LIGO and Virgo.