Flexible and efficient noise characterization is crucial for the precise estimation of gravitational wave parameters. We introduce a fast and accurate Bayesian method for estimating the power spectral density (PSD) of long, stationary time series tailored specifically for LISA data analysis. Our approach models the PSD as a geometric mean of a parametric and a nonparametric component, combining the computational efficiency of 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 during initialization eliminates computationally expensive reversible-jump Markov Chain Monte Carlo, while hierarchical roughness penalty priors prevent overfitting. This design yields stable, flexible PSD estimates with runtimes of minutes instead of hours. Validation on simulated autoregressive AR(4) data demonstrates estimator consistency. It 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 a year of simulated LISA $X$-channel noise, our method achieves relative integrated absolute errors of $\mathcal{O}(10^{-2})$ with computation times less than three minutes, which makes it suitable for iterative analysis pipelines and multi-year mission datasets.

翻译：灵活高效的噪声表征对于引力波参数的精确估计至关重要。本文提出一种快速、准确的贝叶斯方法，专门针对LISA数据分析中的长平稳时间序列进行功率谱密度估计。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平均，既保留了参数模型的计算效率，又具备捕捉理论预期偏差的灵活性。非参数分量通过惩罚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节点布置，避免了计算代价高昂的可逆跳转马尔可夫链蒙特卡罗方法，同时采用分层粗糙度惩罚先验防止过拟合。该设计可在数分钟而非数小时内获得稳定、灵活的功率谱密度估计结果。在模拟自回归AR(4)数据上的验证证明了估计量的一致性。研究表明，相较于无信息基线，良好匹配的参数分量能够降低积分绝对误差，且达到相当精度所需的样条节点更少。将本方法应用于一年期模拟LISA $X$通道噪声数据，在计算时间不足三分钟的情况下实现了$\mathcal{O}(10^{-2})$量级的相对积分绝对误差，这使其适用于迭代分析流程及多年期任务数据集。