Fast, flexible, and accurate evaluation of gravitational-wave Malmquist bias with machine learning

TL;DR

This paper presents a machine learning approach to efficiently and accurately estimate the selection function for gravitational-wave detections, significantly reducing errors and expanding the range of detectable black hole spin models.

Contribution

The authors introduce a novel density estimation method with a pre-processing step that outperforms existing techniques in estimating gravitational-wave selection functions.

Findings

Lower statistical errors at similar computational cost

Probes over 99% of black hole spin models

Reduces uncertainty for more than 80% of models

Abstract

Many astronomical surveys are limited by the brightness of the sources, and gravitational-wave searches are no exception. The detectability of gravitational waves from merging binaries is affected by the mass and spin of the constituent compact objects. To perform unbiased inference on the distribution of compact binaries, it is necessary to account for this selection effect, which is known as Malmquist bias. Since systematic error from selection effects grows with the number of events, it will be increasingly important over the coming years to accurately estimate the observational selection function for gravitational-wave astronomy. We employ density estimation methods to accurately and efficiently compute the compact binary coalescence selection function. We introduce a simple pre-processing method, which significantly reduces the complexity of the required machine learning models. We demonstrate that our method has smaller statistical errors at comparable computational cost than the method currently most widely used allowing us to probe narrower distributions of spin magnitudes. The currently used method leaves $10-50\%$ of the interesting black hole spin models inaccessible; our new method can probe $>99\%$ of the models and has a lower uncertainty for $>80\%$ of the models.