One to many: Comparing single gravitational-wave events to astrophysical populations

Gravitational-wave observations have revealed sources whose unusual properties challenge our understanding of compact-binary formation. Inferring the formation processes that are best able to reproduce such events may therefore yield key astrophysical insights. A common approach is to count the fraction of synthetic events from a simulated population that are consistent with some real event. Though appealing owing to its simplicity, this approach is flawed because it neglects the full posterior information, depends on an ad hoc region that defines consistency, and fails for high signal-to-noise detections. We point out that a statistically consistent solution is to compute the posterior odds between two simulated populations, which crucially is a relative measure, and show how to include the effect of observational biases by conditioning on source detectability. Applying the approach to several gravitational-wave events and simulated populations, we assess the degree to which we can conclude model preference not just between distinct formation pathways but also between subpopulations within a given pathway.