Flexible and accurate noise characterization is crucial for the precise estimation of gravitational-wave parameters. We introduce a Bayesian method for estimating the power spectral density (PSD) of long, stationary time series, explicitly tailored for LISA data analysis. Our approach models the PSD as the geometric mean of a parametric and a nonparametric component, combining the knowledge from parametric models with the flexibility to capture deviations from theoretical expectations. The nonparametric component is expressed by a mixture of penalized B-splines. Adaptive, data-driven knot placement, performed once at initialization, removes the need for reversible-jump Markov chain Monte Carlo, while hierarchical roughness-penalty priors prevent overfitting. Validation on simulated autoregressive AR(4) data demonstrates estimator consistency and shows that well-matched parametric components reduce the integrated absolute error compared to an uninformative baseline, requiring fewer spline knots to achieve comparable accuracy. Applied to one year of simulated LISA X-channel (univariate) noise, our method achieves relative integrated absolute errors of $\mathcal{O}(10^{-2})$, making it suitable for iterative analysis pipelines and multi-year mission data sets.

翻译：灵活且精确的噪声表征对于引力波参数的准确估计至关重要。本文提出一种针对长平稳时间序列功率谱密度（PSD）的贝叶斯估计方法，专为LISA数据分析设计。该方法将PSD建模为参数化分量与非参数化分量的几何平均值，既融合了参数化模型的先验知识，又具备捕捉理论预期偏差的灵活性。非参数化分量通过惩罚B样条混合函数表示。在初始化阶段执行一次自适应数据驱动的节点布置，避免了可逆跳转马尔可夫链蒙特卡罗方法的使用，而分层粗糙度惩罚先验则有效防止过拟合。在模拟自回归AR(4)数据上的验证表明，该估计量具有一致性，且当参数化分量匹配良好时，相较于无信息基线可降低积分绝对误差，同时以更少的样条节点达到相当精度。应用于一年期模拟LISA X通道（单变量）噪声数据时，本方法获得$\\mathcal{O}(10^{-2})$量级的相对积分绝对误差，适用于迭代分析流程及多年期任务数据集。