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

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

TL;DR

The authors address PSD estimation for long, stationary LISA time series lacking quiet-off-source segments by proposing a Bayesian semiparametric model where the PSD is the geometric mean of a parametric component $S_{\text{par}}(f)$ and a nonparametric correction $S_{\text{npar}}(f)$ implemented through a log-$c(f)$ P-spline. They employ fixed-knots P-splines with a hierarchical roughness prior and a blocked Whittle likelihood to enable fast, scalable inference, avoiding RJMCMC. Through AR(4) simulations, they demonstrate that a well-specified parametric template reduces IAE and knot requirements, while the spline correction robustly accommodates misspecification. Applied to a year of simulated LISA X-channel data, the method achieves relative log-PSD errors on the order of ${\cal O}(10^{-2})$ with runtimes of a few minutes, supporting iterative, mission-scale analyses and offering a flexible diagnostic for instrument noise models.

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.

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

TL;DR

The authors address PSD estimation for long, stationary LISA time series lacking quiet-off-source segments by proposing a Bayesian semiparametric model where the PSD is the geometric mean of a parametric component and a nonparametric correction implemented through a log- P-spline. They employ fixed-knots P-splines with a hierarchical roughness prior and a blocked Whittle likelihood to enable fast, scalable inference, avoiding RJMCMC. Through AR(4) simulations, they demonstrate that a well-specified parametric template reduces IAE and knot requirements, while the spline correction robustly accommodates misspecification. Applied to a year of simulated LISA X-channel data, the method achieves relative log-PSD errors on the order of with runtimes of a few minutes, supporting iterative, mission-scale analyses and offering a flexible diagnostic for instrument noise models.

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 , making it suitable for iterative analysis pipelines and multi-year mission data sets.

Paper Structure

This paper contains 7 sections, 16 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. P-spline Model for the Log PSD
  3. Simulation study
  4. Application to LISA Noise
  5. Noise Models
  6. Application of P-spline framework
  7. Discussion

Figures (2)

  • Figure 1: Performance comparison between semi-parametric PSD estimators. (a) PSD estimates for a single realization; (b) IAE distributions across dataset sizes; (c) Sensitivity of IAE to the number of knots. Model 1 (green) and Model 2 (orange) are shown throughout.
  • Figure 2: Power-spectral-density (PSD) estimation for the second-generation Michelson TDI $X$ channel using the OMS parametric noise model. Results are shown for data sets of 3 months, 6 months, and 1 year (light-to-dark red). Top: shaded regions show the middle $90\%$ credible interval (CI) for each observing time. The dashed black curve is the theoretical PSD $S_{\rm X}$, solid purple curve is the OMS parametric PSD, and the gray trace is a representative 5-day block periodogram. Bottom: relative error of the CI of log PSD against $\log(S_{\rm X})$. Longer observation times yield narrower CIs and smaller relative errors.