Bayesian nonparametric estimation of correlated gravitational wave detector network noise using matrix-gamma process priors
arXiv:2607.26619
The paper introduces a Bayesian nonparametric method that directly estimates the correlated noise spectral density matrix of future gravitational‑wave detector networks using matrix‑gamma process priors and adaptive MCMC, avoiding biased signal inference.
Abstract
This paper addresses the important problem of estimating the noise spectral density of next-generation gravitational-wave detectors, such as LISA and the Einstein Telescope (ET), where cross-channel correlations must be accounted for to avoid biased parameter estimation of gravitational-wave signals. Unlike approaches that estimate test-mass and optical-metrology-system noise separately at the single-link level and then map them to the Time-Delay Interferometry (TDI) channels through known transfer functions, we develop a Bayesian nonparametric method that directly estimates the spectral density matrix of the XYZ channels, thereby accommodating additional sources of uncertainty. Our approach combines a flexible matrix-gamma process prior on the matrix-valued coefficients of a Bernstein polynomial basis expansion with a blocked multivariate Whittle likelihood. The prior guarantees Hermitian positive definiteness of the spectral estimate at every frequency. To avoid reversible-jump methods, we use an adaptive Markov chain Monte Carlo (MCMC) algorithm for posterior sampling. The proposed framework can also be used to correct misspecified parametric noise models. Results from a simulation study and simulated correlated-noise data for both LISA and ET demonstrate the effectiveness of the proposed method.