Physics & Astronomy Faculty Publications
Document Type
Article
Publication Date
11-12-2025
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.
Recommended Citation
Franciolini, Gabriele, Mauro Pieroni, Angelo Ricciardone, and Joseph D. Romano. "Likelihoods for stochastic gravitational wave background data analysis." Physical Review D 112, no. 10 (2025): 103516. https://doi.org/10.1103/sjtb-gnz5
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Physical Review D
DOI
10.1103/sjtb-gnz5
Comments
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.