Kavli Affiliate: Lijing Shao
| First 5 Authors: , , , ,
| Summary:
In the era of the next-generation gravitational-wave detectors, signal
overlaps will become prevalent due to high detection rate and long signal
duration, posing significant challenges to data analysis. While effective
algorithms are being developed, there still lacks an integrated understanding
on the statistical properties for the population of overlapping
compact-binary-coalescence signals. For the first time, in order to aid rapid
and robust estimation, we rigorously derive and establish analytical
expressions for the expectation and variance for the number of overlapping
events. This framework is highly extensible, allowing analytical calculation
for more complicated scenarios, such as multi-signal overlaps, overlaps between
different types of sources, and source-dependent thresholds. We also
mathematically prove that the time difference between events in a single
observation run is described by the beta distribution, offering an analytical
prior reference for Bayesian analysis.
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