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.
