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Although gravitational-wave signals from exceptional low-mass compact binarycoalescences, like GW170817, may carry matter signatures that differentiate thesource from a binary black hole system, only one out of every eight eventsdetected by the current Advanced LIGO and Virgo observatories are likely tohave signal-to-noise ratios large enough to measure matter effects, even ifthey are present. Nonetheless, the systems' component masses will generally beconstrained precisely. Constructing an explicit mixture model for the totalrate density of merging compact objects, we develop a hierarchical Bayesiananalysis to classify gravitational-wave sources according to the posterior oddsthat their component masses are drawn from different subpopulations. Accountingfor current uncertainty in the maximum neutron star mass, and adoptingdifferent reasonable models for the total rate density, we examine two recentevents from the LIGO-Virgo Collaboration's third observing run, GW190425 andGW190814. For population models with no overlap between the neutron star andblack hole mass distributions, we typically find that there is a $\gtrsim 70\%$chance that GW190425 was a binary neutron star merger rather than aneutron-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.

Discriminating between Neutron Stars and Black Holes with Imperfect Knowledge of the Maximum Neutron Star Mass