  Black hole masses are tightly correlated with the stellar velocity
dispersions of the bulges which surround them, and slightly less-well
correlated with the bulge luminosity. It is common to use these correlations to
estimate the expected abundance of massive black holes. This is usually done by
starting from an observed distribution of velocity dispersions or luminosities
and then changing variables. This procedure neglects the fact that there is
intrinsic scatter in these black hole mass--observable correlations. Accounting
for this scatter results in estimates of black hole abundances which are larger
by almost an order of magnitude at masses >10^9 M_sun. Including this scatter
is particularly important for models which seek to infer quasar lifetimes and
duty cycles from the local black hole mass function. However, even when scatter
has been accounted for, the M_bh-sigma relation predicts fewer massive black
holes than does the M_bh-L relation. This is because the sigma-L relation in
the black hole samples currently available is inconsistent with that in the
SDSS sample from which the distributions of L or sigma are based: the black
hole samples have smaller L for a given sigma, or larger sigma for a given L.
The sigma-L relation in the black hole samples is similarly discrepant with
that in other samples of nearby early-type galaxies. This suggests that current
black hole samples are biased: if this is a selection rather than physical
effect, then the M_bh-sigma and M_bh-L relations currently in the literature
are also biased from their true values.
