A self-consistent method to estimate the rate of compact binary coalescences with a Poisson mixture model
The recently published GWTC-1 (Abbott B P et al (LIGO Scientific Collaboration and Virgo Collaboration) 2019 Phys. Rev. X 9 031040)—a journal article summarizing the search for gravitational waves (GWs) from coalescing compact binaries in data produced by the LIGO-Virgo network of ground-based detectors during their first and second observing runs—quoted estimates for the rates of binary neutron star, neutron star black hole binary, and binary black hole mergers, as well as assigned probabilities of astrophysical origin for various significant and marginal GW candidate events. In this paper, we delineate the formalism used to compute these rates and probabilities, which assumes that triggers above a low ranking statistic threshold, whether of terrestrial or astrophysical origin, occur as independent Poisson processes. In particular, we include an arbitrary number of astrophysical categories by redistributing, via mass-based template weighting, the foreground probabilities of candidate events, across source classes. We evaluate this formalism on synthetic GW data, and demonstrate that this method works well for the kind of GW signals observed during the first and second observing runs.
© 2020 IOP Publishing Ltd. Received 13 May 2019, revised 13 November 2019; Accepted for publication 5 December 2019; Published 16 January 2020. We thank the LIGO-Virgo Scientific Collaboration for access to data. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation (NSF) and operates under cooperative agreement PHY-0757058. We gratefully acknowledge the support by NSF Grant PHY-1626190 for the UWM computer cluster. We also thank Deep Chatterjee, Shaon Ghosh and Chad Hanna for illuminating discussions. SJK gratefully acknowledges suppport through NSF grant PHY-1607585. SRM thanks the LSSTC Data Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining Grant # 1829740, the Brinson Foundation, and the Moore Foundation.
Submitted - 1903.06881.pdf