  This is the first paper in a series devoted to systematic study of the size
and structure of the broad-line region (BLR) in active galactic nuclei (AGNs)
using reverberation mapping (RM) data. We employ a recently developed Bayesian
approach that statistically describes the variabibility as a damped random walk
process and delineates the BLR structure using a flexible disk geometry that
can account for a variety of shapes, including disks, rings, shells, and
spheres. We allow for the possibility that the line emission may respond
non-linearly to the continuum, and we detrend the light curves when there is
clear evidence for secular variation. We use a Markov Chain Monte Carlo
implementation based on Bayesian statistics to recover the parameters and
uncertainties for the BLR model. The corresponding transfer function is
obtained self-consistently. We tentatively constrain the virial factor used to
estimate black hole masses; more accurate determinations will have to await
velocity-resolved RM data. Application of our method to RM data with Hbeta
monitoring for about 40 objects shows that the assumed BLR geometry can
reproduce quite well the observed emission-line fluxes from the continuum light
curves. We find that the Hbeta BLR sizes obtained from our method are on
average ~20% larger than those derived from the traditional cross-correlation
method. Nevertheless, we still find a tight BLR size-luminosity relation with a
slope of alpha=0.55\pm0.03 and an intrinsic scatter of ~0.18 dex. In
particular, we demonstrate that our approach yields appropriate BLR sizes for
some objects (such as Mrk 142 and PG 2130+099) where traditional methods
previously encountered difficulties.
