  In recent years, there have been significant advances in multi-messenger
astronomy due to the discovery of the first, and so far only confirmed,
gravitational wave event with a simultaneous electromagnetic (EM) counterpart,
as well as improvements in numerical simulations, gravitational wave (GW)
detectors, and transient astronomy. This has led to the exciting possibility of
performing joint analyses of the GW and EM data, providing additional
constraints on fundamental properties of the binary progenitor and merger
remnant. Here, we present a new Bayesian framework that allows inference of
these properties, while taking into account the systematic modeling
uncertainties that arise when mapping from GW binary progenitor properties to
photometric light curves. We extend the relative binning method presented in
Zackay et al. (2018) to include extrinsic GW parameters for fast analysis of
the GW signal. The focus of our EM framework is on light curves arising from
r-process nucleosynthesis in the ejected material during and after merger, the
so called kilonova, and particularly on black hole - neutron star systems. As a
case study, we examine the recent detection of GW190425, where the primary
object is consistent with being either a black hole (BH) or a neutron star
(NS). We show quantitatively how improved mapping between binary progenitor and
outflow properties, and/or an increase in EM data quantity and quality are
required in order to break degeneracies in the fundamental source parameters.
