AI 中文总结
本文针对下一代引力波探测器噪声估计的通道相关性问题，提出基于矩阵伽马过程先验的贝叶斯非参数方法，经模拟验证可有效校正噪声模型偏差。
AI 中文摘要
本文解决了下一代引力波探测器（如LISA和爱因斯坦望远镜（ET））的噪声谱密度估计这一重要问题，必须考虑通道间的相关性以避免引力波信号参数估计出现偏差。与现有方法（在单链路级别分别估计测试质量和光学计量系统的噪声，再通过已知传递函数将其映射到时延干涉测量（TDI）通道）不同，我们开发了一种贝叶斯非参数方法，直接估计XYZ通道的谱密度矩阵，从而容纳额外的不确定性来源。该方法将伯恩斯坦多项式基展开的矩阵值系数上的灵活矩阵伽马过程先验，与分块多元惠特尔似然相结合；该先验保证了每个频率处谱估计的埃尔米特正定性。为避免可逆跳跃方法，我们采用自适应马尔可夫链蒙特卡洛（MCMC）算法进行后验采样。所提框架还可用于校正设定错误的参数化噪声模型。针对LISA和ET的模拟研究及模拟相关噪声数据的结果，证明了所提方法的有效性。
英文摘要
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.
