Bayesian nonparametric estimation of correlated gravitational wave detector network noise using matrix-gamma process priors

2026-07-29

AI Summary

This work addresses the bias in gravitational-wave parameter estimation that arises when inter-channel noise correlations are neglected in next-generation detectors such as LISA and the Einstein Telescope. The authors propose a Bayesian nonparametric approach that, for the first time, directly models the multi-channel noise covariance structure in the frequency domain. By employing a matrix Gamma process prior constructed on Bernstein polynomial bases, the method guarantees that the noise spectral density matrix remains Hermitian positive definite at every frequency. Posterior inference is achieved through a blockwise multivariate Whittle likelihood combined with an adaptive MCMC algorithm. Crucially, this framework requires no prespecified parametric noise model, enabling accurate characterization of noise correlations and their uncertainties, thereby significantly improving the precision of gravitational-wave parameter estimates in simulated data.

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.

Problem

• gravitational-wave detectors
• noise spectral density
• cross-channel correlations
• Bayesian nonparametric estimation
• matrix-gamma process

Innovation

• Bayesian nonparametrics
• matrix-gamma process
• spectral density matrix
• gravitational-wave detectors
• adaptive MCMC