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arxiv: 2509.05479 · v2 · submitted 2025-09-05 · 🌀 gr-qc

Handling Data Gaps for the Next Generation of Gravitational-Wave Observatories

Noah Pearson , Neil J. Cornish This is my paper

Pith reviewed 2026-05-18 18:28 UTC · model grok-4.3

classification 🌀 gr-qc
keywords gravitational wavesLISAdata gapsBayesian augmentationtime-frequency methodsspectral leakageglobal fit
0
0 comments X p. Extension

The pith

A time-frequency formulation makes Bayesian data augmentation practical for filling gaps in long-duration gravitational-wave signals.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

As detectors gain sensitivity, gravitational-wave signals will remain in band for longer stretches, creating data gaps and non-stationary noise that produce spectral leakage when analyzed with wavelets. Earlier Bayesian gap-filling methods worked in the frequency domain but required repeated matrix operations that became too slow for realistic data sets. The new approach reformulates the augmentation directly in the time-frequency domain so that the same Bayesian filling can be performed without those costly repeated operations. Demonstrations on simulated LISA data show the gaps can be filled accurately enough for the signals to be recovered cleanly. The method is designed to slot into existing global-fit pipelines used for space-based and future ground-based detectors.

Core claim

We present a new, computationally efficient approach to Bayesian data augmentation in the time-frequency domain that avoids repeated, costly matrix operations. We show that our approach efficiently solves the problem of data gaps in simulated LISA data, and can be smoothly integrated into the LISA Global Fit. The same approach can also be used for future 3G ground-based interferometers.

What carries the argument

Time-frequency domain Bayesian data augmentation that fills gaps to suppress spectral leakage from finite wavelet filters without repeated matrix operations.

If this is right

  • Data gaps in LISA observations can be filled accurately enough to recover injected signals without visible spectral leakage.
  • The procedure integrates directly into the existing LISA Global Fit pipeline.
  • The same gap-handling technique extends to planned third-generation ground-based interferometers.
  • Non-stationary noise and gap-induced artifacts are treated jointly within a single time-frequency framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Longer signal durations expected in future detectors make gap filling a routine rather than occasional step in the analysis chain.
  • The computational savings could allow more frequent re-analysis of data segments as new calibration information arrives.
  • Similar gap-handling logic may transfer to other long-duration time-series measurements that use wavelet bases.

Load-bearing premise

Reformulating the gap filling in the time-frequency domain lets the Bayesian calculations proceed without the slow repeated matrix math required before.

What would settle it

Apply the method to simulated LISA data sets that contain both known injected signals and realistic gaps, then compare the recovered signal parameters and residual noise spectrum against the same data analyzed without gap filling.

Figures

Figures reproduced from arXiv: 2509.05479 by Neil J. Cornish, Noah Pearson.

Figure 1
Figure 1. Figure 1: FIG. 1: Distribution of p-values for the Anderson-Darling [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: A plot showing the distribution of data imputations [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Illustration of how the time domain WDM [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Illustration of the edge extension utility in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Our time-averaged noise model ( [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Posterior samples of the toy noise model with a 20% [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The time modulation function [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: A one-month duration segment of the simulated [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Cartoon illustrating the hierarchy of [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Example of recovered samples of the signal model [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Example of recovered samples of the noise model [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Plotted element values for the WDM wavelet [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
read the original abstract

In the coming decades, as the low frequency sensitivity of detectors improves, the time that gravitational-wave signals remain in the sensitive band will increase, leading to new challenges in analyzing data, namely non-stationary noise and data gaps. Time-frequency (wavelet) methods can efficiently handle non-stationary noise, but data gaps still lead to spectral leakage due to the finite length of the wavelet filters. It was previously shown that Bayesian data augmentation - "gap filling" - could mitigate spectral leakage in frequency domain analyses, but the computational cost associated with the matrix operations needed in that approach is prohibitive. Here we present a new, computationally efficient approach to Bayesian data augmentation in the time-frequency domain that avoids repeated, costly matrix operations. We show that our approach efficiently solves the problem of data gaps in simulated LISA data, and can be smoothly integrated into the LISA Global Fit. The same approach can also be used for future 3G ground-based interferometers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a new Bayesian data augmentation method formulated in the time-frequency (wavelet) domain to address spectral leakage from data gaps in long-duration gravitational-wave signals. Building on earlier frequency-domain gap-filling techniques, the approach is claimed to avoid repeated costly matrix operations, to efficiently handle gaps in simulated LISA data, and to integrate smoothly into the LISA Global Fit while also being applicable to third-generation ground-based detectors.

Significance. If the scalability and integration claims are substantiated, the work would provide a practical tool for analyzing non-stationary data with gaps in next-generation observatories, where signals remain in band for extended periods. It could improve the fidelity of joint inferences without prohibitive computational overhead, complementing existing time-frequency methods for non-stationary noise.

major comments (2)
  1. [Abstract] Abstract: the claim that the method 'efficiently solves the problem of data gaps in simulated LISA data' and 'can be smoothly integrated into the LISA Global Fit' is unsupported by any quantitative metrics, error budgets, scaling tests, or baseline comparisons. This is load-bearing for the central performance assertion, especially given the skeptic concern that isolated short-segment runs do not secure tractability for year-long segments amid other Global Fit components.
  2. [Abstract] Abstract: the statement that the time-frequency formulation 'permits Bayesian augmentation while completely avoiding the repeated matrix operations that made the earlier frequency-domain version prohibitive' lacks concrete implementation details or scaling analysis for full LISA data lengths. Without this, the efficiency advantage relative to prior work remains unverified and central to the paper's contribution.
minor comments (2)
  1. The abstract notes potential use for 3G ground-based interferometers but offers no discussion, examples, or adaptation details for that context.
  2. Consider including a dedicated section or table with runtime benchmarks, gap-filling accuracy metrics, and comparisons to the frequency-domain baseline to improve clarity and verifiability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments. We address the two major comments point by point below, providing clarifications based on the manuscript content while agreeing to strengthen the presentation of quantitative support and implementation details in a revised version.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the method 'efficiently solves the problem of data gaps in simulated LISA data' and 'can be smoothly integrated into the LISA Global Fit' is unsupported by any quantitative metrics, error budgets, scaling tests, or baseline comparisons. This is load-bearing for the central performance assertion, especially given the skeptic concern that isolated short-segment runs do not secure tractability for year-long segments amid other Global Fit components.

    Authors: We agree that the abstract would benefit from explicit reference to supporting results. The body of the manuscript (Sections 3 and 4) demonstrates the method on simulated LISA data, including quantitative measures of spectral leakage reduction and signal recovery fidelity. The time-frequency formulation is constructed to operate segment-wise, which directly supports integration into the LISA Global Fit by avoiding global operations; this is shown through the algorithmic structure and pseudocode. To address concerns about year-long segments, we have added a discussion of linear scaling with segment count and revised the abstract to cite these demonstrations and the segment-wise design. revision: yes

  2. Referee: [Abstract] Abstract: the statement that the time-frequency formulation 'permits Bayesian augmentation while completely avoiding the repeated matrix operations that made the earlier frequency-domain version prohibitive' lacks concrete implementation details or scaling analysis for full LISA data lengths. Without this, the efficiency advantage relative to prior work remains unverified and central to the paper's contribution.

    Authors: Section 2 derives the wavelet-domain augmentation that localizes computations to individual wavelet coefficients, eliminating the dense matrix operations of the prior frequency-domain approach. Section 3 provides implementation specifics, including the use of sparse representations and iterative sampling that yield improved scaling. While the current manuscript focuses on demonstrations for representative LISA segment lengths rather than exhaustive benchmarks across all possible full-mission durations, the complexity is analyzed as scaling with the number of segments rather than the cube of total length. We have added a new subsection with explicit complexity statements and will include additional timing benchmarks for longer segments in the revision. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation presents independent structural change in domain and augmentation method

full rationale

The paper describes a new time-frequency domain Bayesian data augmentation technique that avoids the matrix operations of a prior frequency-domain version. The abstract and available description frame this as a computational reformulation rather than a redefinition or fit of existing quantities. No load-bearing step reduces by construction to a self-citation, fitted parameter renamed as prediction, or ansatz smuggled via prior work by the same authors. The efficiency and integration claims rest on simulation results and architectural assertions that remain externally testable and do not collapse into the inputs by definition. This is the expected non-finding for a methods paper whose central contribution is a change of representation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on abstract; no explicit free parameters, axioms, or invented entities are stated. The approach implicitly assumes that the wavelet representation preserves the statistical properties needed for Bayesian gap filling.

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