2026 workshop program
Calibrated Selection Functions for Binary Black Holes via Normalizing Flows
The work
Abstract
Accurate selection functions are essential for inferring the astrophysical population of binary black holes from gravitational-wave catalogs. Semi-analytic approaches based on post-Newtonian (PN) amplitude scaling and signal-to-noise ratio thresholds are widely used because they are fast and interpretable, but they neglect spin precession, higher modes, and merger-ringdown physics. We present a conditional normalizing flow trained on a large set of IMRPhenomXPHM waveform simulations in the LIGO-Hanford, Livingston, Virgo three-detector network at design sensitivity, which learns the full distribution of the optimal network SNR conditioned on the binary parameters. An analytic non-central χ² noise model maps this to the observed SNR, yielding calibrated, threshold-agnostic detection probabilities. We benchmark the flow against an exact analytic baseline, two linear-regression semi-analytic models, and a formula-free data-driven baseline that uses no PN extrapolation. The flow matches the exact baseline on calibration, recovers data-driven sensitive volumes across the chirp-mass and effective-spin plane, and corrects a systematic high-mass volume bias inherent to PN-extrapolated semi-analytic methods. The resulting selection function is fast to evaluate, differentiable, and applicable across detector configurations without retraining.