Flexible and Fast Estimation of Binary Merger Population Distributions with Adaptive KDE

Document #:

LIGO-T2100447-v2

Document type:

T - Technical notes

Abstract:

A total of more than 50 binary compact object mergers has been detected by the LIGO-Virgo network in their most recent observing run. The formation channels of these compact objects are still highly uncertain: to make progress we require a range of methods to characterize their population properties. The Bayesian hierarchical methods mainly employed so far become more computationally expensive as the size of event catalogs increases, and assume simple functional forms for the source distribution. Here we propose a fast and flexible method to reconstruct the population of LIGO-Virgo binary mergers without such assumptions. Under some conditions (sufficiently high statistics, sufficiently low individual event measurement error relative to width of population features) a kernel density estimator (KDE) reconstruction of the mass distribution from parameter estimation (PE) median masses will be sufficiently accurate. The method we are proposing improves the accuracy and flexibility of kernel density estimation (KDE) by using adaptive bandwidth (awKDE) and cross-validation to obtain an optimal bandwidth. We apply awKDE to publicly released parameter estimatesfor binary mergers in O1, O2, and O3a, in combination with a fast polynomial fit of search sensitivity, to obtain a non-parametric estimate of the mass distribution for comparison with established Bayesian hierarchical methods.

Files in Document:

• method document (awKDEmethod.pdf, 2.6 MB)

Topics:

• Compact Binaries

Authors:

• Jam Sadiq
• Thomas Dent
• Daniel Wysocki

Keywords:

compact binary merger black hole mass spin redshift population

Notes and Changes:

added references, edits to rate and mass/distance sections