Extend the joint spline framework to realistic LISA data complexities

Extend the Bayesian joint spline framework for LISA instrumental-noise and stochastic gravitational-wave-background inference to handle time-varying arm lengths, data gaps, and non-stationary noise, potentially using a time-frequency treatment.

Background

The study evaluates the joint log-P-spline framework under an idealized LISA configuration with equal arm lengths, stationary noise, and perfectly known response and transfer functions. These assumptions simplify inference but omit operational and instrumental effects expected in realistic LISA data.

The authors explicitly leave the extension to time-varying arm lengths, data gaps, and non-stationary noise for future investigations, noting that such complexities will likely require a time-frequency formulation rather than the stationary frequency-domain treatment used in the paper.

References

Extending such a framework (including computation of SNRs~\citealp{Digman:2022jmp}, and parameter estimation~\citealp{DuTF}) to the full network with cross-detector correlations is promising for providing a more precise and physically sound assessment, while a rigorous treatment of residual non-Gaussianity~\citep{Racine:2007gv,Buscicchio:2024wwm} and a time-dependent covariance for year-long observations remain for future work.

— Correlated Galactic Confusion Foreground for the LISA-Taiji-TianQin Network and Its Implications for Resolvable Source Analysis  (2609.16477 - Du et al., 15 Sep 2026) in Section Conclusion and outlook

However, in a more general context, data gaps are expected to frequently occur in the data of space detectors, and a thorough treatment of them should also be deferred to future studies.

— Correlated Galactic Confusion Foreground for the LISA-Taiji-TianQin Network and Its Implications for Resolvable Source Analysis  (2609.16477 - Du et al., 15 Sep 2026) in Section Conclusion and outlook

Extending the model to handle realistic complexities, such as time-varying arm lengths, data gaps, or non-stationary noise, will likely require a time-frequency treatment, which we leave for future investigations.

— Bayesian P-spline recovery of stochastic gravitational-wave backgrounds in LISA  (2608.20629 - Aimen et al., 21 Aug 2026) in Section V, Discussion

We also leave the case where the instrumental noise deviates from its theoretical expectation to future work.

— Bayesian P-spline recovery of stochastic gravitational-wave backgrounds in LISA  (2608.20629 - Aimen et al., 21 Aug 2026) in Section V, Discussion