In this work we perform a Bayesian statistical fit to estimate the mass-to-distance ratio and the recessional redshift of 10 different black holes hosted at the centre of active galactic nuclei, namely the galaxies NGC 5765b, NGC 6323, UGC 3789, CGCG 074-064, ESO 558-G009, NGC 2960, NGC 6264, NGC 4388, J0437+2456 and NGC 2273. Our general relativistic method makes use of the positions in the sky and frequency shift observations of water megamasers circularly orbiting the central black hole on their accretion disks. This approach also allows us to quantify the gravitational redshift which is not considered in a Newtonian analysis. The gravitational redshift of the megamasers closest to the black hole is found to be within the range 1-6 km/s. The order of the fitted black hole masses corresponds to supermassive black holes and lies on the range 106 − 107M/odot;.