Bayesian power spectral density estimation for LISA noise based on P-splines with a parametric boost

Abstract: 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.