Obtaining Statistical Significance of Gravitational Wave Signals in Hierarchical Search

Gravitational Wave (GW) astronomy has experienced remarkable growth in recent years, driven by advancements in ground-based detectors. While detecting compact binary coalescences (CBCs) has become routine, searching for more complex ones, such as mergers involving eccentric and precessing binaries and sub-solar mass binaries, has presented persistent challenges. These challenges arise from using the standard matched filtering algorithm, whose computational cost increases with the dimensionality and size of the template bank. This urges the pressing need for faster search pipelines to efficiently identify GW signals, leading to the emergence of the hierarchical search strategy. This method looks for potential candidate events using a sparse template bank in the first stage, followed by dense templates around potential events in the second stage. Although the hierarchical search speeds up the standard PyCBC analysis by more than a factor of 20, as demonstrated in a previous work~\cite{kanchan_hierarchical}, assigning statistical significance to detected signals was done in a heuristic way. In this article, we present a robust approach for background estimation in a two-stage hierarchical search. Our method models background triggers from time-shifted triggers in a two-detector network, extrapolating to higher statistic values. Through an extensive injection campaign for a population of simulated signals on real data, we test the effectiveness of our background estimation approach. The results show our method achieves a sensitive volume-time product comparable to the standard two-detector PyCBC search. This equivalence holds for an inverse false alarm rate of 10 years and chirp mass $1.4-10~\text{M}_\odot$, substantially reducing computational cost with a remarkable speed-up of nearly 13 times compared to PyCBC analysis.Comment: 13 pages, 10 figure