  We describe the general problem of estimating black hole masses of AGN by
calculating the conditional probability distribution of M_BH given some set of
observables. Special attention is given to the case where one uses the AGN
continuum luminosity and emission line widths to estimate M_BH, and we outline
how to set up the conditional probability distribution of M_BH given the
observed luminosity, line width, and redshift. We show how to combine the broad
line estimates of M_BH with information from an intrinsic correlation between
M_BH and L, and from the intrinsic distribution of M_BH, in a manner that
improves the estimates of M_BH. Simulation was used to assess how the
distribution of M_BH inferred from the broad line mass estimates differs from
the intrinsic distribution, and we find that this can lead to an inferred
distribution that is too broad. We use these results and a sample of 25 sources
that have recent reverberation mapping estimates of AGN black hole masses to
investigate the effectiveness of using the C IV emission line to estimate M_BH
and to indirectly probe the C IV region size--luminosity (R--L) relationship.
We estimated M_BH from both C IV and H-Beta for a sample of 100 sources,
including new spectra of 29 quasars. We find that the two emission lines give
consistent estimates if one assumes R \propto L^{1/2}_{UV} for both lines.
