  Joint gravitational wave (GW) and electromagnetic (EM) observations, as a key
research direction in multi-messenger astronomy, will provide deep insight into
the astrophysics of a vast range of astronomical phenomena. Uncertainties in
the source sky location estimate from gravitational wave observations mean
follow-up observatories must scan large portions of the sky for a potential
companion signal. A general frame of joint GW-EM observations is presented by a
multi-messenger observational triangle. Using a Bayesian approach to
multi-messenger astronomy, we investigate the use of galaxy catalogue and host
galaxy information to reduce the sky region over which follow-up observatories
must scan, as well as study its use for improving the inclination angle
estimates for coalescing binary compact objects. We demonstrate our method
using a simulated neutron stars inspiral signal injected into simulated
Advanced detectors noise and estimate the injected signal sky location and
inclination angle using the Gravitational Wave Galaxy Catalogue. In this case
study, the top three candidates in rank have $72\%$, $15\%$ and $8\%$ posterior
probability of being the host galaxy, receptively. The standard deviation of
cosine inclination angle (0.001) of the neutron stars binary using
gravitational wave-galaxy information is much smaller than that (0.02) using
only gravitational wave posterior samples.
