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We jointly constrain the luminosity function (LF) and black hole massfunction (BHMF) of broad-line quasars with forward Bayesian modeling in thequasar mass-luminosity plane, based on a homogeneous sample of ~ 58,000 SDSSDR7 quasars at z ~ 0.3-5. We take into account the selection effect of thesample flux limit; more importantly, we deal with the statistical scatterbetween true BH masses and FWHM-based single-epoch virial mass estimates, aswell as potential luminosity-dependent biases of these mass estimates. The LFis tightly constrained in the regime sampled by SDSS, and makes reasonablepredictions when extrapolated to ~ 3 magnitudes fainter. Downsizing is seen inthe model LF. On the other hand, we find it difficult to constrain the BHMF towithin a factor of a few at z>~0.7 (with MgII and CIV-based virial BH masses).This is mainly driven by the unknown luminosity-dependent bias of these massestimators and its degeneracy with other model parameters, and secondly drivenby the fact that SDSS quasars only sample the tip of the active BH populationat high redshift. Nevertheless, the most likely models favor a positiveluminosity-dependent bias for MgII and possibly for CIV, such that at fixedtrue BH mass, objects with higher-than-average luminosities have over-estimatedFWHM-based virial masses. There is tentative evidence that downsizing alsomanifests itself in the active BHMF, and the BH mass density in broad-linequasars contributes an insignificant amount to the total BH mass density at alltimes. Within our model uncertainties, we do not find a strong BH massdependence of the mean Eddington ratio; but there is evidence that the meanEddington ratio (at fixed BH mass) increases with redshift.

The Demographics of Broad-Line Quasars in the Mass-Luminosity Plane. I. Testing FWHM-Based Virial Black Hole Masses