Living on the edge: Testing for compact population features at the edges of parameter space

TL;DR

This paper presents a truncated Gaussian mixture model approach to accurately detect population features near parameter boundaries, reducing bias and computational cost in astrophysical data analysis.

Contribution

The authors introduce a novel truncated Gaussian mixture model framework that improves boundary feature inference, demonstrated on gravitational wave data with lower computational costs.

Findings

Accurately estimates zero-spin binary black hole fractions.

Reduces bias in boundary population feature detection.

Achieves similar results to previous methods with less computation.

Abstract

Many astrophysical population studies involve parameters that exist on a bounded domain, such as the dimensionless spins of black holes or the eccentricities of planetary orbits, both of which are confined to $[0, 1]$. In such scenarios, we often wish to test for distributions clustered near a boundary, e.g., vanishing spin or orbital eccentricity. Conventional approaches -- whether based on Monte Carlo, kernel density estimators, or machine-learning techniques -- often suffer biases at the boundaries. These biases stem from sparse sampling near the edge, kernel-related smoothing, or artifacts introduced by domain transformations. We introduce a truncated Gaussian mixture model framework that substantially mitigates these issues, enabling accurate inference of narrow, edge-dominated population features. While our method has broad applications to many astronomical domains, we consider gravitational wave catalogs as a concrete example to demonstrate its power. In particular, we maintain agreement with published constraints on the fraction of zero-spin binary black hole systems in the GWTC-3 catalog -- results originally derived at much higher computational cost through dedicated reanalysis of individual events in the catalog. Our method can achieve similarly reliable results with a much lower computational cost. The method is publicly available in the open-source packages gravpop and truncatedgaussianmixtures.