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We perform a statistical inference of the astrophysical population of binaryblack hole (BBH) mergers observed during the first two observing runs ofAdvanced LIGO and Advanced Virgo, including events reported in the GWTC-1 andIAS catalogs. We derive a novel formalism to fully and consistently account forevents of arbitrary significance. We carry out a software injection campaign toobtain a set of mock astrophysical events subject to our selection effects, anduse the search background to compute the astrophysical probabilities $p_{\rmastro}$ of candidate events for several phenomenological models of the BBHpopulation. We emphasize that the values of $p_{\rm astro}$ depend on both theastrophysical and background models. Finally, we combine the information fromindividual events to infer the rate, spin, mass, mass-ratio and redshiftdistributions of the mergers. The existing population does not discriminatebetween random spins with a spread in the effective spin parameter, and a smallbut nonzero fraction of events from tidally-torqued stellar progenitors. Themass distribution is consistent with one having a cutoff at $m_{\rm max} =41^{+10}_{-5}\,\rm M_\odot$, while the mass ratio favors equal masses; the meanmass ratio $\bar q> 0.67$. The rate shows no significant evolution withredshift. We show that the merger rate restricted to BBHs with a primary massbetween 20 and $30\, \rm M_\odot$, and a mass ratio $q > 0.5$, and at $z \sim0.2$, is 1.5 to $5.3\,{\rm Gpc^{-3} yr^{-1}}$ (90\% c.l.); these bounds aremodel independent and a factor of $\sim 3$ tighter than that on the local rateof all BBH mergers, and hence are a robust constraint on all progenitor models.Including the events in our catalog increases the Fisher information about theBBH population by $\sim 47\%$, and tightens the constraints on populationparameters.

Binary Black Hole Mergers from LIGO/Virgo O1 and O2: Population Inference Combining Confident and Marginal Events