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arXiv · 2510.00533

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

Nazeela Aimen·Patricio Maturana-Russel·Avi Vajpeyi·Nelson Christensen·Renate Meyer
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Abstract

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.

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Nazeela Aimen, Patricio Maturana-Russel, Avi Vajpeyi, Nelson Christensen, Renate Meyer. 2025-10-01. Bayesian power spectral density estimation for LISA noise based on penalized splines with a parametric boost. https://doi.org/10.1103/dcb6-1jsl

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