Aimen, NazeelaMaturana-Russel, PatricioVajpeyi, AviChristensen, NelsonMeyer, Renate2026-01-142026-01-142026-01-09Physical Review D, ISSN: 2470-0010 (Print); 2470-0029 (Online), American Physical Society (APS), 113(2). doi: 10.1103/dcb6-1jsl2470-00102470-0029http://hdl.handle.net/10292/20494Flexible 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 Laser Interferometer Space Antenna (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 a reversible-jump Markov chain Monte Carlo, while hierarchical roughness-penalty priors prevent overfitting. Validation on simulated autoregressive (AR) data of order 4 [AR(4)] 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 𝒪⁡(10ˉ²), making it suitable for iterative analysis pipelines and multiyear mission data sets.This is the Author's Accepted Manuscript of an article published in Physical Review D. The Version of Record is available at DOI: 10.1103/dcb6-1jsl49 Mathematical Sciences4905 Statisticsgravitational wavesPSD estimationP-splinesLISAJournal ArticleOpenAccess10.1103/dcb6-1jsl