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  • Open Access

Likelihoods for stochastic gravitational wave background data analysis

Gabriele Franciolini1,*, Mauro Pieroni1,2,†, Angelo Ricciardone3,4,‡, and Joseph D. Romano5,§

  • 1CERN, Theoretical Physics Department, Esplanade des Particules 1, Geneva 1211, Switzerland
  • 2Instituto de Estructura de la Materia (IEM), CSIC, Serrano 121, 28006 Madrid, Spain
  • 3Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo Bruno Pontecorvo 3, Pisa I-56127, Italy
  • 4INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, Pisa I-56127, Italy
  • 5Department of Physics and Astronomy, University of Texas Rio Grande Valley, One West University Boulevard, Brownsville, Texas 78520, USA

  • *Contact author: gabriele.franciolini@cern.ch
  • †Contact author: mauro.pieroni@csic.es
  • ‡Contact author: angelo.ricciardone@unipi.it
  • §Contact author: joseph.romano@utrgv.edu
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Phys. Rev. D 112, 103516 – Published 12 November, 2025

DOI: https://doi.org/10.1103/sjtb-gnz5

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 cross-correlation 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.

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Phys. Rev. D 112, 103516– Published 12 November, 2025
  • Received 11 June 2025
  • Accepted 22 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN.

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