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：灵活准确的噪声表征对于精确估计引力波参数至关重要。我们提出一种用于估算长平稳时间序列功率谱密度的贝叶斯方法，该方法专为LISA数据分析设计。该方法将功率谱密度建模为参数分量与非参数分量的几何均值，既融合了参数模型的知识，又具备捕捉理论预期偏差的灵活性。非参数分量由惩罚B样条的混合模型表示。在初始化阶段一次完成的适应性数据驱动节点布设消除了对可逆跳跃马尔可夫链蒙特卡罗的需求，而层次化粗糙度惩罚先验则能防止过拟合。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，且匹配良好的参数分量相比无信息基线能降低综合绝对误差，在实现同等精度时所需样条节点更少。将该方法应用于为期一年的模拟LISA X通道（单变量）噪声时，综合绝对相对误差达$\mathcal{O}(10^{-2})$量级，适用于迭代分析流程及多任务数据集的处理。