[Paper Review] Fast, flexible, and accurate evaluation of Malmquist bias with machine learning: Preparing for the pending flood of gravitational-wave detections

C. Talbot, E. Thrane|arXiv (Cornell University)|Dec 3, 2020

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper introduces a fast, flexible, and accurate machine learning approach to compute the gravitational-wave selection function, reducing model complexity via a novel pre-processing step. When applied to LIGO-Virgo GWTC-2 data, the method yields a 1σ steeper mass ratio distribution and a 10% higher inferred binary black hole rate of $\mathcal{R}_{\mathrm{BBH}} = 32^{+11}_{-9}\,\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, demonstrating that selection function estimation significantly impacts population inference.

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 a range of machine learning 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. As a demonstration of our method, we reproduce and extend the results from the recent LIGO--Virgo analysis of events from their second gravitational-wave transient catalog (GWTC-2). While qualitatively consistent with previous work, we find that the method used to compute the selection function noticeably affects the inferred population. The most significant change is a $1\sigma$ increase in the steepness of the mass ratio distribution and an $\sim10\%$ increase in the inferred rate, $\mathcal{R}_{\mathrm{BBH}} = 32^{+11}_{-9}\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, when using our new method. Including spin effects in the selection function does not significantly impact the results with current uncertainties.

Motivation & Objective

• To address the growing challenge of Malmquist bias in gravitational-wave astronomy as detection rates increase.
• To develop a computationally efficient and accurate method for estimating the compact binary coalescence selection function.
• To reduce the complexity of machine learning models used for selection function estimation through a novel pre-processing technique.
• To re-evaluate GWTC-2 results using the new method and assess the impact on population inference parameters.
• To investigate whether including spin effects in the selection function alters current population inferences under existing uncertainties.

Proposed method

• A range of machine learning models are trained to estimate the gravitational-wave selection function for compact binary coalescences.
• A pre-processing method is introduced that simplifies the input space, significantly reducing model complexity and training time.
• The selection function is computed as a function of source parameters, including mass, mass ratio, and spin, to account for detectability variations.
• The method is validated by reproducing and extending the GWTC-2 analysis, using the same data and population model.
• The approach enables fast and flexible evaluation of selection effects across different population models and data sets.
• The impact of including spin in the selection function is quantified using current observational uncertainties.

Experimental results

Research questions

• RQ1 How does the choice of selection function estimation method affect the inferred population parameters of binary black holes?
• RQ2 To what extent does the inclusion of spin in the selection function alter the inferred binary black hole merger rate and mass distribution?
• RQ3 Can a pre-processing step significantly reduce the complexity of machine learning models used for selection function estimation without sacrificing accuracy?
• RQ4 How do the results from the new method compare quantitatively with the original GWTC-2 analysis?
• RQ5 What is the impact of improved selection function modeling on the inferred steepness of the mass ratio distribution?

Key findings

• The new method increases the inferred binary black hole merger rate to $\mathcal{R}_{\mathrm{BBH}} = 32^{+11}_{-9}\,\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, representing a 10% increase compared to previous estimates.
• The mass ratio distribution is found to be 1σ steeper when using the new selection function estimation method.
• Including spin effects in the selection function does not lead to significant changes in the inferred population parameters given current uncertainties.
• The pre-processing step reduces model complexity, enabling faster and more efficient training while maintaining high accuracy.
• The results demonstrate that the method used to compute the selection function has a measurable and non-negligible impact on population inference.
• The method provides a scalable and flexible framework for future gravitational-wave population studies with increasing event rates.