  Although gravitational-wave signals from exceptional low-mass compact binary
coalescences, like GW170817, may carry matter signatures that differentiate the
source from a binary black hole system, only one out of every eight events
detected by the current Advanced LIGO and Virgo observatories are likely to
have signal-to-noise ratios large enough to measure matter effects, even if
they are present. Nonetheless, the systems' component masses will generally be
constrained precisely. Constructing an explicit mixture model for the total
rate density of merging compact objects, we develop a hierarchical Bayesian
analysis to classify gravitational-wave sources according to the posterior odds
that their component masses are drawn from different subpopulations. Accounting
for current uncertainty in the maximum neutron star mass, and adopting
different reasonable models for the total rate density, we examine two recent
events from the LIGO-Virgo Collaboration's third observing run, GW190425 and
GW190814. For population models with no overlap between the neutron star and
black hole mass distributions, we typically find that there is a $\gtrsim 70\%$
chance that GW190425 was a binary neutron star merger rather than a
neutron-star--black-hole merger. On the other hand, we find that there is a
$\lesssim 6\%$ chance that GW190814 involved a slowly spinning neutron star,
regardless of our assumed population model.
