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Gravitational wave measurements will provide insight into the population ofcoalescing compact binaries throughout the universe. We describe anddemonstrate a flexible parametric method to infer the event rate as a functionof compact binary parameters, accounting for Poisson error and selectionbiases. Using concrete synthetic data based on projections for LIGO and Virgo'sO3 run, we discuss how well GW measurements could constrain the mass and spindistribution of coalescing neutron stars and black holes in the near future,within the context of several phenomenological models described in this work.We demonstrate that only a few tens of events can enable astrophysicallysignificant constraints on the spin magnitude and orientation distribution ofBHs in merging binaries. We discuss how astrophysical priors or othermeasurements can inform the interpretation of future measurements. Usingpublicly-available results, we estimate the event rate versus mass for binaryblack holes. To connect to previously-published work, we provide estimatesincluding reported O2 BBH candidates, making several unwarranted butsimplifying assumptions for the sensitivity of the network and compleness ofthe reported set of events. Consistent with prior work, we find BHs in binarieslikely have low natal spin. With available results and a population favoringlow spin, we can't presently constrain the typical misalignments of the binaryblack hole population. All of the tools described in this work are publiclyavailable and ready-to-use to interpret real or synthetic LIGO data, and tosynthesize projected data from future observing runs.

Reconstructing phenomenological distributions of compact binaries via gravitational wave observations