[Paper Review] Non-parametric inference of the population of compact binaries from gravitational wave observations using binned Gaussian processes

Anarya Ray, Ignacio Magaña Hernandez+3 more|arXiv (Cornell University)|Apr 17, 2023

Pulsars and Gravitational Waves Research71 references4 citations

TL;DR

This paper introduces a binned Gaussian process framework for nonparametric inference of compact binary populations from gravitational wave data, simultaneously modeling component mass and redshift distributions while capturing correlations between them. The method enables robust, data-driven detection of features like mass peaks and redshift evolution with minimal parametric assumptions, validated on simulated and real GWTC-3 data with consistent, accurate reconstructions across binning resolutions.

ABSTRACT

The observation of gravitational waves from multiple compact binary coalescences by the LIGO-Virgo-KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, non-parametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational wave data in the presence of significant measurement uncertainties, while making very few assumptions on the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing non-parametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can re-construct the underlying distributions of component masses and redshifts. We also re-analyze public LIGO-Virgo-KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and non-parametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO-Virgo-KAGRA detector network in their first 3 observing runs), without making any assumptions about the specific nature of these correlations.

Motivation & Objective

• To develop a nonparametric, data-driven method for inferring the population distributions of compact binary masses and redshifts from gravitational wave observations.
• To simultaneously model mass and redshift distributions while capturing correlations between them, without assuming a specific functional form.
• To reduce reliance on parametric assumptions that may miss unmodeled features in the underlying population distributions.
• To enable accurate inference in the presence of significant measurement uncertainties and Monte Carlo sampling noise.
• To validate the method on simulated data and reanalyze public GWTC-3 data, comparing with existing parametric and nonparametric approaches.

Proposed method

• Employs a binned Gaussian process model to represent the joint distribution of component masses and redshifts, with bins defined in log-mass and redshift space.
• Uses a non-Gaussian likelihood to account for measurement uncertainties and detection sensitivity in gravitational wave data.
• Applies a hierarchical Bayesian framework to infer hyperparameters of the Gaussian process, including length scales that control smoothness.
• Implements marginalization over Monte Carlo uncertainties in a computationally efficient way, avoiding likelihood cuts and ensuring robustness.
• Uses a prior on the population rate density that is consistent with cosmological volume and redshift evolution.
• Validates the method by testing on simulated data with known underlying distributions and comparing with alternative inference schemes.

Experimental results

Research questions

• RQ1 Can a nonparametric method detect features in the component mass distribution of compact binaries without assuming a specific functional form?
• RQ2 How well can the method reconstruct the redshift evolution of the merger rate and its correlation with mass distribution?
• RQ3 Does the model remain robust and consistent when the number of bins is increased, indicating convergence of the inference?
• RQ4 What is the impact of correlations between mass and redshift on population inference, and can the model detect them without prior assumptions?
• RQ5 How does the method compare in accuracy and consistency to existing parametric and nonparametric population inference techniques on real GWTC-3 data?

Key findings

• The binned Gaussian process model successfully reconstructs the underlying mass and redshift distributions in simulated data with high accuracy, even with significant measurement uncertainties.
• The inferred posterior distributions of the GP length scale remain stable when binning resolution is doubled, indicating convergence and robustness.
• The method produces consistent population constraints across different binning choices, confirming that resolution beyond feature detection does not alter the inference.
• Reanalysis of GWTC-3 data reveals no strong evidence for significant correlations between mass and redshift in the binary black hole population, within the model's sensitivity.
• The model correctly marginalizes over Monte Carlo uncertainties without computational penalty, unlike some existing approaches.
• The framework enables detection of substructure in the mass spectrum and redshift evolution without parametric assumptions, supporting data-driven discovery of astrophysical features.