Accurate pulsar timing array likelihoods: better low-rank covariance for gravitational wave background
Abstract
In pulsar timing array analyses, the stochastic process describing the gravitational wave background is typically modeled using a Fourier basis at discrete frequencies with an interval ∼ 0.1 yr−1, with a diagonal Fourier-domain covariance determined by the power spectral density at the corresponding frequencies. Although this rank-reduced modeling significantly accelerates likelihood evaluation and provides a good approximation in many scenarios, it can lead to biased parameter inference because it is insensitive to spectral features on scales smaller than ∼ 0.1 yr−1. We introduce a better construction of the low-rank covariance for low-frequency processes by maximizing the log-likelihood averaged over an ensemble of realizations drawn from the true model likelihood. In this approach, the basis-domain covariance matrix is sensitive to the entire model spectrum and is generally non-diagonal. Using two mock datasets, we demonstrate improved likelihood accuracy and more faithful recovery of spectral features compared to the conventional Fourier-diagonal model. Benchmark tests show that this new model requires a computational cost comparable to that of the conventional approach.
Related
- Constructing likelihoods for a non-Gaussian gravitational-wave background
- Close Pulsar Pairs See Dark Matter Substructure through the Gravitational-Wave Background
- A Delayed Rejection Reversible Jump Markov Chain Monte Carlo Method for Multi-Resolution Maps of the Stochastic Gravitational Wave Background with Pulsar Timing Array Data
- Prior volume effect inflates the gravitational-wave background in pulsar timing arrays
- Comparing gravitational wave background predictions from cosmological simulations to pulsar timing observations
BibTeX
@misc{deng2026accurate,
title = {{Accurate pulsar timing array likelihoods: better low-rank covariance for gravitational wave background}},
author = {Heling Deng and Ken D. Olum and Rutger van Haasteren},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33444},
eprint = {2610.33444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33444},
}
RIS
TY - UNPB
TI - Accurate pulsar timing array likelihoods: better low-rank covariance for gravitational wave background
AU - Heling Deng
AU - Ken D. Olum
AU - Rutger van Haasteren
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33444
UR - https://arxiv.org/abs/2610.33444
AB - In pulsar timing array analyses, the stochastic process describing the gravitational wave background is typically modeled using a Fourier basis at discrete frequencies with an interval ∼ 0.1 yr^−1, with a diagonal Fourier-domain covariance determined by the power spectral density at the corresponding frequencies. Although this rank-reduced modeling significantly accelerates likelihood evaluation and provides a good approximation in many scenarios, it can lead to biased parameter inference because it is insensitive to spectral features on scales smaller than ∼ 0.1 yr^−1. We introduce a better construction of the low-rank covariance for low-frequency processes by maximizing the log-likelihood averaged over an ensemble of realizations drawn from the true model likelihood. In this approach, the basis-domain covariance matrix is sensitive to the entire model spectrum and is generally non-diagonal. Using two mock datasets, we demonstrate improved likelihood accuracy and more faithful recovery of spectral features compared to the conventional Fourier-diagonal model. Benchmark tests show that this new model requires a computational cost comparable to that of the conventional approach.
ER -