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arxiv: 2604.16039 · v1 · submitted 2026-04-17 · 🌀 gr-qc · astro-ph.IM

Measuring the rate of glitches in interferometric gravitational wave detectors with a hierarchical Bayesian model

Gregory Ashton , Colm Talbot , Andrew Lundgren , Ann-Kristin Malz , Joseph Areeda This is my paper

Pith reviewed 2026-05-10 07:54 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.IM
keywords gravitational wavesglitcheshierarchical Bayesian inferencerate estimationLIGOnoise artifactsobserving run
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The pith

A hierarchical Bayesian model measures glitch rates in gravitational wave detectors down to low signal-to-noise without arbitrary thresholds.

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

The paper introduces a hierarchical Bayesian model for estimating the rate of glitches, which are non-Gaussian noise artifacts in ground-based gravitational wave detectors. This improves on traditional trigger-counting methods by allowing measurements at lower signal strengths where glitches blend with Gaussian noise, as long as the glitch population is modeled correctly. The approach incorporates quantile compression for efficient hierarchical inference and basis functions to capture how the rate changes over time. Validation on simulated data with injected glitches confirms the method, and application to LIGO-Virgo-KAGRA's fourth observing run yields time-resolved rate estimates over 24-hour periods. These estimates align with trigger counts but provide finer detail and enable calculation of coincident glitch probabilities to check candidate events.

Core claim

The central claim is that a hierarchical Bayesian model can measure the glitch rate down into the low signal-to-noise regime without contamination from the Gaussian noise background, provided the population is accurately modelled, using novel features like hierarchical inference with quantile compression and time-domain rate estimation via basis functions.

What carries the argument

Hierarchical inference with quantile compression (HIQC) as an approximation for the hierarchical recycled likelihood, together with basis function fitting for the time-dependent rate.

If this is right

  • The glitch rate can be measured without imposing an arbitrary signal-to-noise ratio threshold.
  • Time-resolved inferences of the glitch rate over a 24 h period are obtained from the data.
  • Individual-detector rate estimates can be transformed into a coincident glitch probability for multi-detector events.
  • This allows validation that certain retracted gravitational-wave candidates are likely pairs of coincident glitches.

Where Pith is reading between the lines

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

  • This method could reduce bias in astrophysical parameter estimation by better identifying and accounting for glitches overlapping with signals.
  • Patterns in the time-varying glitch rate might correlate with known environmental or instrumental factors, suggesting targeted mitigation strategies.
  • Extending the model to include signal populations jointly could lead to more accurate detection and characterization in future analyses.

Load-bearing premise

The population of glitches must be accurately modelled to separate the rate measurement from the Gaussian noise background.

What would settle it

Observing a significant mismatch between the model's low-SNR rate estimate and the high-SNR trigger count in a controlled simulation where the population model is known to be correct.

Figures

Figures reproduced from arXiv: 2604.16039 by Andrew Lundgren, Ann-Kristin Malz, Colm Talbot, Gregory Ashton, Joseph Areeda.

Figure 1
Figure 1. Figure 1: A histogram of the counts of Omicron trigger SNRs over one day of data (2023-08-18) in the LIGO Livingston detector during O4a, along with time-frequency spectrograms (created using GWpy: Macleod et al. 2021) of triggers selected from representative regions of the distribution: vertical dashed lines denote their SNR. The spectrograms cover a time span of 1 s and a frequency range from 20 Hz to 1 kHz. any t… view at source ↗
Figure 3
Figure 3. Figure 3: Validation of the HIQC method for a toy model comparing the full likelihood, Eq. (24) with the HIQC likelihood, Eq. (29) varying the number of quantiles. Then, for the recycled hyperlikelihood, the evidence term in Eq. (9) is computed from Z (𝑑®|𝜗, 𝑀G) = Ö𝑁𝑠 𝑖=0 Z (𝑑𝑖 |𝜗, 𝑀ˆ G) 1 𝑀𝑖 ∑︁𝑀𝑖 ℓ=1 𝜋(𝜃 ℓ 𝑖 |𝜗) 𝜋(𝜃 ℓ 𝑖 |𝜗ˆ) . (24) where 𝑀𝑖 is the number of samples from the 𝑖th posterior distribu￾tion. We note that… view at source ↗
Figure 4
Figure 4. Figure 4: The whitened strain and posterior predictive distribution from six realisations of the simulated data used in our validation study. In black, we show the data, after whitening, which includes coloured Gaussian noise alongside a glitch simulated by glitchflow. On top, we add the prediction of the antiglitch model under the maximum posterior estimate (red curve) and shaded blue bands showing the 68, 95, and … view at source ↗
Figure 5
Figure 5. Figure 5: The distribution of Log Bayes factors (ln 𝐵, i.e., the ratio of evidence for the antiglitch model against the coloured-Gaussian noise only hypoth￾esis) calculated for data containing coloured Gaussian noise and glitches simulated with glitchflow. In the left-hand figure, we show the distribution of ln 𝐵 as a function of time, with the marker size scaled by ln 𝐵 and vertical lines marking the times of simul… view at source ↗
Figure 6
Figure 6. Figure 6: Estimates of the glitch rate calculated over the 1 hour of data presented in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Inferred amplitude distributions for noise-only (blue) and glitch (orange) simulations, along with the predicted power-law scaling (green). scaling parameter. While it does not reflect the expected distribution of glitches in real data, it allows us to validate the method in a regime where the glitch and noise distributions are cleanly separated. Finally, in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Posterior distributions inferred from the level-II analysis of the data presented in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Distribution of the inferred maximum 𝜌mf and median amplitudes measured from the Level-I analysis of the data simulated for the sensitivity study. We separate the distributions into the inferences from data segments including a glitch (blue) and data segments with only Gaussian noise (orange). above a minimum 𝜌mf of ∼ 6, but biased toward an underestimate of the rate below. The cause of this can be unders… view at source ↗
Figure 11
Figure 11. Figure 11: The inferred glitch rate taken from a 1000 s set of data randomly sampling from the signal and noise distributions in [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Natural-log-evidence as a function of the number of bases used in the level-II analyses applied to simulated data in which the glitch rate suddenly changes. All values are given relative to the maximum, which is found at 𝑁basis = 6 with a spline order of 2. 3.4 Time-dependent rate analysis To validate the time-dependent level-II inference method described in Section 2.6, we follow the data-generating proc… view at source ↗
Figure 13
Figure 13. Figure 13: The time-dependent glitch rate inferred from simulated data in which the glitch rate suddenly changes. A solid black line marks the true glitch rate while red vertical bars denote the time of simulated glitches. The blue solid line marks the median rate inferred from the time-dependent level-II analysis using splines with 𝑁basis = 8; a blue band marks the 90% interval on the inferred distribution. Similar… view at source ↗
Figure 15
Figure 15. Figure 15: A comparison of the SNR taken from omicron triggers presented in [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The glitch rate inferred from the data presented in [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The time-dependent glitch rate inferred from the glitch-only analysis (blue) and glitch and population model (orange) for 1 d of data from [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: A histogram of the compute time for all Level-I analyses performed for the day of LLO data. We colour each histogram bin by the average ln 𝐵 of analyses within the bin. However, in the case of an ambiguous candidate (e.g., where the FAR or other significance estimate lies near typical thresholds used to separate signals from noise), additional investigations may be useful to determine if a candidate is as… view at source ↗
Figure 19
Figure 19. Figure 19: The glitch rate posterior for LHO (blue) and LLO (red) inferred from 1 h of data surrounding the candidate GW230630_070659. Shaded re￾gions indicate the 90% credible interval. 0.0 0.2 0.4 0.6 0.8 1.0 Probability of coincident glitches 0 2 4 6 8 Density [PITH_FULL_IMAGE:figures/full_fig_p014_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The probability of a pair of coincident glitches 𝑃CG, estimated using Eq. (35), samples from posterior distribution on the rates from [PITH_FULL_IMAGE:figures/full_fig_p014_20.png] view at source ↗
read the original abstract

Ground-based gravitational wave detectors are now routinely surveying the dark Universe, finding hundreds of collisions between compact objects such as black holes and neutron stars. However, terrestrial non-Gaussian noise artefacts, commonly known as glitches, reduce the sensitivity to signals and can overlap signals, producing biased astrophysical inferences. We introduce a hierarchical Bayesian model to measure the glitch rate, which improves upon existing trigger-counting methods in its capacity to measure the rate down into the low signal-to-noise regime without contamination from the Gaussian noise background, provided the population is accurately modelled. The methodology builds on standard hierarchical inference, but includes several novel features, including hierarchical inference with quantile compression (HIQC), a generic approximation method for the hierarchical recycled likelihood, and a time-domain rate estimated by fitting basis functions. We validate the methodology using simulated data with injected glitches and then apply it to data from the fourth LIGO-Virgo-KAGRA observing run, demonstrating time-resolved inferences of the glitch rate over a 24 h period. The inferred glitch rate is consistent with estimates from trigger counts, but does not require an arbitrary threshold and provides a more fine-grained view of the temporal behaviour. Finally, we demonstrate how our individual-detector rate estimates can be transformed into a coincident glitch probability and utilise this to validate that the retracted gravitational-wave candidate GW230630_070659 is likely a pair of coincident glitches.

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

3 major / 2 minor

Summary. The paper introduces a hierarchical Bayesian model to estimate the glitch rate in gravitational-wave detectors. It claims this approach measures rates into the low-SNR regime without Gaussian-noise contamination (conditional on accurate population modeling), using novel elements including hierarchical inference with quantile compression (HIQC), a recycled-likelihood approximation, and basis-function fitting for time-resolved rates. The method is validated on simulated injections and applied to O4 data to produce 24-hour time-resolved rate inferences, which are stated to be consistent with trigger counts but threshold-free and finer-grained; it is also used to assess a retracted candidate (GW230630_070659) as likely coincident glitches.

Significance. If the central claim holds under realistic conditions, the work offers a principled, threshold-free alternative to trigger counting for glitch-rate estimation. This could improve detector characterization, reduce contamination in astrophysical inferences, and provide time-resolved diagnostics. The use of hierarchical inference, HIQC, and basis-function modeling for temporal structure are technically interesting extensions of standard methods in the field.

major comments (3)
  1. [Validation on simulated data] Validation section (simulated injections): The reported tests inject glitches drawn from the exact population model assumed in the inference. No sensitivity analyses with deliberately misspecified populations (e.g., altered SNR distributions, different morphology priors, or non-stationary rates) are described. Because the headline advantage over trigger counting is explicitly conditional on accurate population modeling, this omission leaves the robustness of the low-SNR rate posterior untested and is load-bearing for the central claim.
  2. [O4 data analysis] Application to O4 data and population modeling: The manuscript fits basis functions and employs HIQC/recycled-likelihood approximations, yet provides no quantitative assessment of how rate posteriors respond when the assumed glitch population deviates from the true distribution. Without such checks, it is unclear whether the reported consistency with trigger counts persists or whether low-SNR inferences absorb model mismatch as bias.
  3. [Time-resolved rate model] Time-domain rate estimation via basis functions: The choice of basis and regularization are not shown to be robust; if the basis is too flexible, the inferred rate could absorb noise fluctuations rather than reflect true glitch occurrence, undermining the claim of a cleaner low-SNR measurement.
minor comments (2)
  1. [Abstract and §2] The abstract and introduction should explicitly state the functional form of the glitch population model (e.g., SNR distribution, morphology priors) used in both simulations and O4 analysis.
  2. [Methodology] Notation for the hierarchical recycled likelihood and HIQC compression could be clarified with a short schematic diagram or explicit equation linking the compressed likelihood to the full hierarchical posterior.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments highlight important aspects of robustness that strengthen the central claims of the work. We address each major comment below and will incorporate revisions to provide the requested sensitivity analyses and checks.

read point-by-point responses

  1. Referee: [Validation on simulated data] Validation section (simulated injections): The reported tests inject glitches drawn from the exact population model assumed in the inference. No sensitivity analyses with deliberately misspecified populations (e.g., altered SNR distributions, different morphology priors, or non-stationary rates) are described. Because the headline advantage over trigger counting is explicitly conditional on accurate population modeling, this omission leaves the robustness of the low-SNR rate posterior untested and is load-bearing for the central claim.

    Authors: We agree that the validation demonstrates recovery under the assumed model but does not probe robustness to misspecification, which is relevant given the conditional nature of the low-SNR claim. In the revised manuscript we will add a dedicated sensitivity section that injects glitches from deliberately misspecified populations, including altered SNR power-law indices, varied morphology priors, and non-stationary rates. These tests will quantify any resulting bias or variance inflation in the recovered rate posteriors, thereby directly addressing the load-bearing aspect of the central claim. revision: yes

  2. Referee: [O4 data analysis] Application to O4 data and population modeling: The manuscript fits basis functions and employs HIQC/recycled-likelihood approximations, yet provides no quantitative assessment of how rate posteriors respond when the assumed glitch population deviates from the true distribution. Without such checks, it is unclear whether the reported consistency with trigger counts persists or whether low-SNR inferences absorb model mismatch as bias.

    Authors: The O4 analysis relies on consistency with trigger counts as an external cross-check under the fitted population model. We acknowledge the absence of explicit mismatch quantification. The revision will include a quantitative assessment in which the population hyperparameters are deliberately varied around the fiducial values; the resulting changes to the 24-hour rate posteriors will be reported, allowing readers to evaluate the stability of both the trigger-count consistency and the low-SNR inferences under plausible deviations. revision: yes

  3. Referee: [Time-resolved rate model] Time-domain rate estimation via basis functions: The choice of basis and regularization are not shown to be robust; if the basis is too flexible, the inferred rate could absorb noise fluctuations rather than reflect true glitch occurrence, undermining the claim of a cleaner low-SNR measurement.

    Authors: The basis functions were selected to capture expected diurnal and shorter-term variations in glitch rates while the regularization was chosen to penalize unphysically rapid fluctuations. We have not, however, presented explicit robustness tests against alternative bases or regularization strengths. The revised manuscript will add a supplementary analysis comparing results obtained with different basis families (e.g., cubic splines versus Fourier) and a range of regularization hyperparameters, demonstrating that the inferred time-resolved rates remain stable and do not exhibit spurious absorption of noise. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained statistical inference

full rationale

The paper introduces a hierarchical Bayesian model for glitch rate inference that extends standard hierarchical methods with approximations (HIQC, recycled-likelihood, basis-function time-domain rate). The rate posterior is obtained by conditioning on an assumed glitch population model and data; this is not equivalent to the inputs by construction. The low-SNR advantage is explicitly conditional on accurate population modeling, but that is a modeling assumption rather than a definitional loop or fitted-input renaming. No self-citation chains, uniqueness theorems, or ansatzes are invoked to force the central result. Validation on matched simulations tests the pipeline under its stated assumptions without reducing the claimed measurement to a tautology. The derivation remains independent of the target rate value.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the model rests on standard hierarchical Bayesian assumptions plus the explicit caveat that the glitch population must be accurately modelled. No specific free parameters or invented entities are named.

axioms (1)
  • domain assumption The glitch population can be accurately modelled
    Explicitly stated as the condition under which the low-SNR measurement works without Gaussian contamination.

pith-pipeline@v0.9.0 · 5560 in / 1266 out tokens · 40077 ms · 2026-05-10T07:54:43.437808+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    Measuringtherateofglitchesin interferometricgravitationalwavedetectorswithahierarchicalBayesian model

    Aasi J., et al., 2015, Classical and Quantum Gravity, 32, 074001 Abac A. G., et al., 2025a, arXiv e-prints, p. arXiv:2508.18079 Abac A. G., et al., 2025b, arXiv e-prints, p. arXiv:2508.18081 Abac A. G., et al., 2025c, arXiv e-prints, p. arXiv:2508.18082 Abbott R., et al., 2023, Physical Review X, 13, 041039 Abramovici A., et al., 1992, Science, 256, 325 A...

    work page doi:10.5281/zenodo.19630780 2015

  2. [2]

    This paper has been typeset from a TEX/LATEX file prepared by the author. MNRAS000, 1–16 (2026) Measuring the glitch rate17 Figure A1.Time-frequency spectrograms of LLO data segments in our study when theOmicrontrigger SNR is greater than 10, butln𝐵from the level-I analysis is negative, indicating the antiglitch model did not find evidence for a signal. M...

    work page 2026