Measuring angular N-point correlations of binary black hole merger gravitational-wave events with hierarchical Bayesian inference

Advanced LIGO and Virgo have detected ten binary black hole mergers by the end of their second observing run. These mergers have already allowed constraints to be placed on the population distribution of black holes in the Universe, which will only improve with more detections and increasing sensitivity of the detectors. In this paper we develop techniques to measure the angular distribution of black hole mergers by measuring their statistical N-point correlations through hierarchical Bayesian inference. We apply it to the special case of two-point angular correlations using a Legendre polynomial basis on the sky. Building on the mixture model formalism introduced in Ref.[1] we show how one can measure two-point correlations with no threshold on significance, allowing us to target the ensemble of sub-threshold binary black hole mergers not resolvable with the current generation of ground based detectors. We also show how one can use these methods to correlate gravitational waves with other probes of large scale angular structure like galaxy counts, and validate both techniques through simulations.