Probing Extremal Gravitational-Wave Events with Coarse-Grained Likelihoods

When analyzing populations of event, we often wish to quantify whether the most extreme events are consistent with the rest of the population. In this paper, we demonstrate that previous outlier analyses suffer from a subtle bias and derive a rigorous method for identifying and quantifying outliers. Using a simple toy model, we show the efficacy of our method and verify that the secondary object in GW190814 is an outlier with respect to the observed binary black hole population.