Beyond Gaussian Assumptions: A new robust statistical framework for gravitational-wave data analysis

TL;DR

This paper introduces a robust statistical framework using hyperbolic likelihoods for gravitational-wave data analysis, effectively handling non-Gaussian noise and outliers, and demonstrating improved accuracy in real-world scenarios.

Contribution

It extends previous heavy-tailed likelihood methods to the full frequency domain, enhancing robustness in gravitational-wave data analysis beyond Gaussian assumptions.

Findings

Hyperbolic likelihood performs comparably to Whittle likelihood in Gaussian noise.

Framework shows increased robustness with non-Gaussian noise in real data.

Provides more accurate parameter estimations in challenging noise conditions.

Abstract

Many traditional algorithms applied in gravitational-wave astronomy rely on the assumption of Gaussian noise, a condition not always met. To meet this need, this study extends a robust statistical framework, advancing previous work on heavy-tailed likelihoods, that adapts the hyperbolic likelihood method for full frequency domain applications. The framework is designed to maintain high performance under ideal conditions while improving robustness against non-Gaussian noise and outliers in real-world data. We demonstrate the efficacy of this approach through two key case studies. The first case study analyzes a massive black hole binary merger in simulated Laser Interferometer Space Antenna (LISA) data with Gaussian noise, showing that the extended hyperbolic likelihood method performs comparably to the more commonly used Whittle likelihood. The second case study examines a stellar-mass black hole binary merger using real ground-based gravitational-wave data containing non-Gaussian noise or overlapping signals, where our framework exhibits increased robustness and yields more accurate parameter estimations. Our results show that the hyperbolic likelihood better captures the true noise distribution, providing a flexible and physically motivated alternative for GW data analysis across current and future detectors.