  Fast radio bursts (FRBs) are mysterious astrophysical transients whose origin
and mechanism remain unclear. Compact object mergers may be a promising channel
to produce some FRBs. Neutron star-black hole (NSBH) mergers could produce FRBs
through mechanisms involving neutron star tidal disruption or magnetospheric
disturbances. This could present an opportunity for multi-messenger
gravitational-wave observations, providing new insight into the nature of FRBs
and nuclear matter. However, some of the gravitational-wave signals may be
marginal detections with signal-to-noise ratios < 8 or have large sky location
and distance uncertainties, making it less straightforward to confidently
associate an FRB with the gravitational-wave signal. One must therefore take
care to avoid a false positive association. We demonstrate how to do this with
simulated data. We calculate the posterior odds -- a measurement of our
relative belief for a common versus unrelated origin of a coincident NSBH and
FRB. We find that a coincident FRB+NSBH from a common source can yield a
statistically significant posterior odds in a network with at least two
observatories, but only if we require a coincidence in time and and sky
location, rather than time alone. However, we find that for our model, we
require a network signal-to-noise ratio greater than 10 to be confident in the
common-source detection, when using a threshold of ln odds > 8. We suggest that
a coincident NSBH+FRB detection could help distinguish between FRB engines by
discriminating between disrupting and non-disrupting models.
