Reconstructing the Edges: Testing for compact population features at the edges of parameter space

Often we are interested in testing certain hypotheses about populations of objects in the universe, where we find that the event-level parameters are theoretically bound to be within a range. A common example is dimensionless black hole (BH) spin, which ranges between 0 and 1 (black holes with a larger spin simply cannot exist). In these situations we may may want to test whether there is a significant sub-population entirely within the parameter’s edge value (e.g. a population of BHs with very close to zero spin, or a beyond-GR parameter being exactly 0). Current methods that employ Monte Carlo methods to evaluate population models may find a biased result when testing for such hypothesis due to a lack of posterior samples near the edge. We introduce a new framework using Truncated Gaussian Mixture models to reduce the bias near the edge and show how one can accurately test such hypothesis. As an example we test whether there is any evidence that majority of black holes have negligibly small spins.