  We present a novel Probabilistic Flux Variation Gradient (PFVG) approach to
to separate the contributions of active galactic nuclei (AGN) and host galaxies
in the context of photometric reverberation mapping (PRM) of AGN. We explored
the ability of recovering the fractional contribution in a model-independent
way using the entire set of light curves obtained through different filters and
photometric apertures simultaneously. The method is based on the observed bluer
when brighter phenomenon that is attributed to the superimposition of a
two-component structure; the red host galaxy, which is constant in time, and
the varying blue AGN. We describe the PFVG mathematical formalism and
demonstrate its performance using simulated light curves and available PRM
observations. The new probabilistic approach is able to recover host-galaxy
fluxes to within 1% precision as long as the light curves do not show a
significant contribution from time delays. This represents a significant
improvement with respect to previous applications of the traditional FVG method
to PRM data. The proposed PFVG provides an efficient and accurate way to
separate the AGN and host-galaxy luminosities in PRM monitoring data. The
method will be especially helpful in the case of large upcoming photometric
survey telescopes such as the public optical/near-infrared Legacy Survey of
Space and Time (LSST) at the Vera C. Rubin Observatory. Finally, we have made
the algorithms freely available as part of our Julia PFVG package.
