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 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 $\mathcal{O}({10}^{-2})$, making it suitable for iterative analysis pipelines and multiyear mission data sets.

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• Gravitational wave detection
• Gravitational waves
• Noise
• Data analysis
• Gravitational wave detectors
• Metropolis algorithm