  The recently published GWTC-1 - 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.
