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This is the first paper in a series devoted to systematic study of the sizeand structure of the broad-line region (BLR) in active galactic nuclei (AGNs)using reverberation mapping (RM) data. We employ a recently developed Bayesianapproach that statistically describes the variabibility as a damped random walkprocess and delineates the BLR structure using a flexible disk geometry thatcan account for a variety of shapes, including disks, rings, shells, andspheres. We allow for the possibility that the line emission may respondnon-linearly to the continuum, and we detrend the light curves when there isclear evidence for secular variation. We use a Markov Chain Monte Carloimplementation based on Bayesian statistics to recover the parameters anduncertainties for the BLR model. The corresponding transfer function isobtained self-consistently. We tentatively constrain the virial factor used toestimate black hole masses; more accurate determinations will have to awaitvelocity-resolved RM data. Application of our method to RM data with Hbetamonitoring for about 40 objects shows that the assumed BLR geometry canreproduce quite well the observed emission-line fluxes from the continuum lightcurves. We find that the Hbeta BLR sizes obtained from our method are onaverage ~20% larger than those derived from the traditional cross-correlationmethod. Nevertheless, we still find a tight BLR size-luminosity relation with aslope of alpha=0.55\pm0.03 and an intrinsic scatter of ~0.18 dex. Inparticular, we demonstrate that our approach yields appropriate BLR sizes forsome objects (such as Mrk 142 and PG 2130+099) where traditional methodspreviously encountered difficulties.

A Bayesian Approach to Estimate the Size and Structure of the Broad-line Region in Active Galactic Nuclei Using Reverberation Mapping Data