Dirichlet Process Gaussian-mixture model: An application to localizing coalescing binary neutron stars with gravitational-wave observations

We report on the Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability densities and compute credible volumes with a minimal set of assumptions. We illustrate its effectiveness by reconstructing posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are $\sim10^4$--$10^5~\mathrm{Mpc^3}$ corresponding to $\sim10^2$--$10^3$ potential host galaxies. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.