AI 中文总结
本研究提出平均场SGVB方法，用于长时长多变量LISA噪声的谱密度估计，其计算成本远低于HMC，且估计结果与HMC及Welch方法一致，为该类分析提供了可扩展的贝叶斯途径。
AI 中文摘要
对于未来的空间引力波探测器（如LISA），估计其谱密度矩阵颇具挑战性，原因在于数据持续时间长，且多个时间延迟干涉测量通道间存在相关的仪器噪声。本研究针对长时长多变量谱密度估计，探究了一种专门的平均场随机梯度变分贝叶斯（SGVB）流程以实现快速后验近似。基于已有的分块Whittle似然方法的本征基表示，该后验模型采用Cholesky分解来表示逆谱密度矩阵，并利用余弦基函数对由此产生的频率相关项进行建模，同时为基函数系数分配了带折扣的正则化马蹄先验。我们将平均场SGVB作为独立的后验近似方法进行测试，与针对同一后验模型的哈密顿量蒙特卡洛（HMC）方法对比。在基于自回归和滑动平均过程的模拟研究中，SGVB生成的后验中位数谱估计与HMC得到的结果相近，但计算成本大幅降低。随后我们将该方法应用于两个时长为一年、固定延迟、平稳、仅含噪声的LISA模拟数据，结果显示，在LISA分析频段内，SGVB的谱密度估计与HMC及Welch估计一致，同时所需计算量显著更少。这些结果表明，SGVB为长时长多变量LISA噪声分析的谱密度估计提供了一种可扩展的贝叶斯方法。
英文摘要
Estimating spectral density matrices for future space-based gravitational-wave detectors such as LISA is challenging due to the long duration of the data and the correlated instrumental noise across multiple time-delay interferometry channels. In this work, we investigate a specialized mean-field stochastic gradient variational Bayes (SGVB) procedure for fast posterior approximation in long-duration multivariate spectral density estimation. Based on the existing eigenbasis representation of the blocked Whittle likelihood approach, the posterior model applies a Cholesky factorization to represent the inverse spectral density matrix and models the resulting frequency-dependent entries with cosine basis functions, with a discounted regularized horseshoe prior assigned to the basis coefficients. We test mean-field SGVB as a stand-alone posterior approximation by comparing it with Hamiltonian Monte Carlo (HMC) targeting the same posterior model. In simulation studies based on autoregressive and moving average processes, SGVB produces posterior median spectral estimates close to those obtained from HMC at substantially lower computational cost. We then apply the method to two one-year, fixed-delay, stationary, noise-only LISA simulations and show that the SGVB spectral density estimates are consistent with HMC and Welch estimates across the LISA analysis band, while requiring substantially less computation. These results demonstrate that SGVB provides a scalable Bayesian approach to spectral density estimation for long-duration multivariate LISA noise analysis.
