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

Argyro Sasli, Minas Karamanis, Nikolaos Karnesis, Michael W. Coughlin, Vuk Mandic, Uroš Seljak, Nikolaos Stergioulas

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.

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

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.
Paper Structure (14 sections, 13 equations, 13 figures, 7 tables)

This paper contains 14 sections, 13 equations, 13 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Statistical Framework
  3. Data model and residuals in GW analysis
  4. Noise-weighted inner product and Gaussian likelihood
  5. Hyperbolic likelihood formulation
  6. Analysis
  7. Sampling strategy
  8. LISA scenario: Simulated Gaussian noise
  9. Ground-based detector scenario: Real noise
  10. Multiple sources of BBH
  11. Glitches
  12. Conclusion & Discussion
  13. Gaussian vs. Whittle in the LISA band
  14. Supplementary details of the LIGO cases

Figures (13)

  • Figure 1: PSD analysis in the LISA band.
  • Figure 2: Cornerplots using the ${\cal W}$ (blue) and the ${\cal H}$ (pink) likelihood. This case correspond to a source of 357 SNR for one-year data (see Table \ref{['tab:models']}). Units follow Table \ref{['tab:models']}.
  • Figure 3: Posterior distributions obtained with the Hyperbolic compared to (a) Gaussian and (b) Whittle likelihoods. Each panel shows split violin plots for the most affected key binary parameters, namely chirp mass $\mathcal{M}~[M_{\odot}]$ and luminosity distance. This case refers to the data with the long-lasting BBH injected. The hyperbolic likelihood systematically reduces bias.
  • Figure 4: Similar to Fig. \ref{['fig:violin_long']}, but for the case with the seven low-SNR BBH injections..
  • Figure 5: Q-plot for 1165578732.45 trigger time with the BBH injection. The red dashed line correspond to the glitch time and the green one to the injected signal.
  • ...and 8 more figures