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 variability 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 H \beta 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 H \beta BLR sizes obtained from our method are on average \sim 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 \pm 0.03 and an intrinsic scatter of \sim 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 .