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Coalescing compact binaries emitting gravitational wave (GW) signals, asrecently detected by the Advanced LIGO-Virgo network, constitute a populationover the multi-dimensional space of component masses and spins, redshift, andother parameters. Characterizing this population is a major goal of GWobservations and may be approached via parametric models. We demonstratehierarchical inference for such models with a method that accounts foruncertainties in each binary merger's individual parameters, for mass-dependentselection effects, and also for the presence of a second population ofcandidate events caused by detector noise. Thus, the method is robust topotential biases from a contaminated sample and allows us to extractinformation from events that have a relatively small probability ofastrophysical origin.

Digging the population of compact binary mergers out of the noise