Likelihoods for Stochastic Gravitational Wave Background Data Analysis

2025/05/30 by Gabriele Franciolini, Franciolini, Gabriele, Mauro Pieroni +5 · 3 citations
Earth and Planetary Sciences · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2505.24695

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a systematic study of likelihood functions used for Stochastic Gravitational Wave Background (SGWB) searches. By dividing the data into many short segments, one customarily takes advantage of the Central Limit Theorem to justify a Gaussian crosscorrelation likelihood. We show, with a hierarchy of ever more realistic examples, beginning with a single frequency bin and one detector, and then moving to two and three detectors with white and colored signal and noise, that approximating the exact Whittle likelihood by various Gaussian alternatives can induce systematic biases in the estimation of the SGWB parameters. We derive several approximations for the full likelihood and identify regimes where Gaussianity breaks down. We also discuss the possibility of conditioning the full likelihood on fiducial noise estimates to produce unbiased SGWB parameter estimation. We show that for some segment durations and bandwidths, particularly in space-based and pulsar-timing arrays, the bias can exceed the statistical uncertainty. Our results provide practical guidance for segment choice, likelihood selection, and data-compression strategies to ensure robust SGWB inference in current and next-generation gravitational wave detectors.

Citations

• The MeerKAT Pulsar Timing Array: the first search for gravitational waves with the MeerKAT radio telescope
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• Fundamentals of Statistical Signal Processing: Estimation Theory

Cited by

• Cosmic Variance in Anisotropy Searches at Pulsar Timing Arrays
• A flexible, GPU-accelerated approach for the joint characterization of LISA instrumental noise and Stochastic Gravitational Wave Backgrounds
• Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia

Related

• Detection methods for non-Gaussian gravitational wave stochastic backgrounds
• Is your stochastic signal really detectable?
• Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects
• Characterization of non-Gaussian stochastic signals with heavier-tailed likelihoods
• Uncovering stochastic gravitational-wave backgrounds with LISA