Flexible and fast estimation of binary merger population distributions with an adaptive kernel density estimator

The LIGO Scientific, Virgo and KAGRA Collaborations recently released the third gravitational wave transient catalog or GWTC-3, significantly expanding the number of gravitational wave signals. To address the---still uncertain---formation channels of the source compact binaries, their population properties must be characterized. The computational cost of the Bayesian hierarchical methods employed thus far scales with the size of the event catalogs, and such methods have until recently assumed fixed functional forms for the source distribution. Here we propose a fast and flexible method to reconstruct the population of LIGO-Virgo merging black hole (BH) binaries without such assumptions. For sufficiently high event statistics and sufficiently low individual event measurement error (relative to the scale of population features) a kernel density estimator (KDE) reconstruction of the event distribution will be accurate. We improve the accuracy and flexibility of KDE for finite event statistics using an adaptive bandwidth KDE (awKDE). We apply awKDE to publicly released parameter estimates for 44 significant (69) BH binary mergers in GWTC-2 (GWTC-3), in combination with a fast polynomial fit of search sensitivity, to obtain a nonparametric estimate of the mass distribution, and compare to Bayesian hierarchical methods. We also demonstrate a robust peak detection algorithm based on awKDE and use it to calculate the significance of the apparent peak in the BH mass distribution around $35\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$. We find such a peak is very unlikely to have occurred if the true distribution is a featureless power-law (significance of $3.6\ensuremath{\sigma}$ for confident GWTC-2 BBH events, $3.0\ensuremath{\sigma}$ for confident GWTC-3 BBH events).