  Characterizing a planet detected by microlensing is hard if the planetary
signal is weak or the lens-source relative trajectory is far from caustics.
However, statistical analyses of planet demography must include those planets
to accurately determine occurrence rates. As part of a systematic modeling
effort in the context of a $>10$-year retrospective analysis of MOA's survey
observations to build an extended MOA statistical sample, we analyze the light
curve of the planetary microlensing event MOA-2014-BLG-472. This event provides
weak constraints on the physical parameters of the lens, as a result of a
planetary anomaly occurring at low magnification in the light curve. We use a
Bayesian analysis to estimate the properties of the planet, based on a refined
Galactic model and the assumption that all Milky Way's stars have an equal
planet-hosting probability. We find that a lens consisting of a
$1.9^{+2.2}_{-1.2}\,\mathrm{M}_\mathrm{J}$ giant planet orbiting a
$0.31^{+0.36}_{-0.19}\,\mathrm{M}_\odot$ host at a projected separation of
$0.75\pm0.24\,\mathrm{au}$ is consistent with the observations and is most
likely, based on the Galactic priors. The lens most probably lies in the
Galactic bulge, at $7.2^{+0.6}_{-1.7}\mathrm{kpc}$ from Earth. The accurate
measurement of the measured planet-to-host star mass ratio will be included in
the next statistical analysis of cold planet demography detected by
microlensing.
