Understanding the geometry and kinematics of the broad line region (BLR) of active galactic nuclei (AGN) is important to estimate black hole masses in AGN and study the accretion process. The technique of reverberation mapping (RM) has provided estimates of BLR size for more than 100 AGN now, however, the structure of the BLR has been studied for only a handful number of objects. Towards this, we investigated the geometry of the BLR for a large sample of 57 AGN using archival RM data. We performed systematic modeling of the continuum and emission line light curves using a Markov Chain Monte Carlo method based on Bayesian statistics implemented in PBMAP (Parallel Bayesian code for reverberation-MAPping data) code to constrain BLR geometrical parameters and recover velocity integrated transfer function. We found that the recovered transfer functions have various shapes such as single-peaked, double-peaked and top-hat suggesting that AGN have very different BLR geometries. Our model lags are in general consistent with that estimated using the conventional cross-correlation methods. The BLR sizes obtained from our modeling approach is related to the luminosity with a slope of 0.583 (+/-) 0.026 and 0.471 (+/-) 0.084 based on H{beta} and H{alpha} lines, respectively. We found a non-linear response of emission line fluxes to the ionizing optical continuum for 93% objects. The estimated virial factors for the AGN studied in this work range from 0.79 to 4.94 having a mean at 1.78 (+/-) 1.77 consistent with the values found in the literature.
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