Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise

研究问题: 如何估计平稳多元时间序列随频率变化的交叉谱矩阵，保证正定性并校准不确定性，同时检验简化的对角噪声假设是否可靠？
方法与思路: 作者对逆谱矩阵采用频率变化的 Cholesky 分解和惩罚样条先验，结合分块 Whittle 似然、温度化校准及 NUTS 后验采样。
材料陈述的贡献: 摘要称模拟中可恢复对角与交叉谱结构，误差随样本量下降；LISA 模拟噪声应用显示对角简化在对称情形接近完整模型，在非对称情形明显失效。
阅读关注点: 应核对平稳性及 Whittle 近似条件、样条先验和温度参数选择，并检查可信区间覆盖、RISE 指标及两类 LISA 噪声配置。
阅读边界: 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要的性能证据来自合成基准与公开模拟数据，不能直接推断真实 LISA 观测中的表现。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

We present a Bayesian P-spline method for estimating the frequency-dependent cross-spectral density matrix of stationary multivariate time series. The inverse spectral matrix is parametrised through its frequency-varying Cholesky decomposition, which guarantees Hermitian positive definiteness at every frequency. Each real log-diagonal entry and each real and imaginary off-diagonal entry is given an independent penalised B-spline prior that controls smoothness. Inference uses a blocked, coarse-grained Whittle likelihood with safe-Bayes $η$ -tempering to stabilise posterior calibration, sampled by the No-U-Turn Sampler from a variational initialisation. On synthetic VAR(2) benchmarks with known ground truth, the method recovers both diagonal and cross-spectral structure, attains near-nominal credible-interval coverage, and achieves a relative integrated squared (Frobenius) error (RISE) that decreases with sample size. We then apply the method to publicly released simulated LISA time-delay interferometry (TDI) data in two noise configurations. In the idealised symmetric case, the full multivariate model and a reduced model that assumes a diagonal AET noise covariance agree to within $\sim10^{-3}$ in RISE. Under realistic noise that is asymmetric across the six Movable Optical Sub-Assemblies (MOSAs), the AET-diagonal assumption fails by more than an order of magnitude in RISE ( $\sim\!3.3\!\times\!10^{-2}$ versus $\sim\!10^{-3}$ ), whereas the full multivariate model recovers the cross-spectral structure.We present a Bayesian P-spline method for estimating the frequency-dependent cross-spectral density matrix of stationary multivariate time series. The inverse spectral matrix is parametrised through its frequency-varying Cholesky decomposition, which guarantees Hermitian positive definiteness at every frequency. Each real log-diagonal entry and each real and imaginary off-diagonal entry is given an independent penalised B-spline prior that controls smoothness. Inference uses a blocked, coarse-grained Whittle likelihood with safe-Bayes $η$-tempering to stabilise posterior calibration, sampled by the No-U-Turn Sampler from a variational initialisation. On synthetic VAR(2) benchmarks with known ground truth, the method recovers both diagonal and cross-spectral structure, attains near-nominal credible-interval coverage, and achieves a relative integrated squared (Frobenius) error (RISE) that decreases with sample size. We then apply the method to publicly released simulated LISA time-delay interferometry (TDI) data in two noise configurations. In the idealised symmetric case, the full multivariate model and a reduced model that assumes a diagonal AET noise covariance agree to within $\sim10^{-3}$ in RISE. Under realistic noise that is asymmetric across the six Movable Optical Sub-Assemblies (MOSAs), the AET-diagonal assumption fails by more than an order of magnitude in RISE ($\sim\!3.3\!\times\!10^{-2}$ versus $\sim\!10^{-3}$), whereas the full multivariate model recovers the cross-spectral structure.

摘要来源：arXiv

笔记与分组

分类依据与纠错

Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise

作者的期刊发表依据

代码、数据与补充材料

谱密度矩阵的多元贝叶斯 P 样条估计及 LISA TDI 噪声应用

原文摘要

同方向的基础文献

同方向的基础文献