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Modelling noise in gravitational-wave observatories with transdimensional models

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A transdimensional Bayesian noise model, tPowerBilby, fits LIGO and Virgo noise better than standard estimates and shifts some astrophysical parameter credible intervals by up to 7%.

desk verdict Useful transdimensional noise-modeling tool for LIGO/Virgo; the 7% parameter shifts are real but best framed as an estimate of noise-model systematics, not a precisely measured effect. read the letter →

arxiv 2501.03285 v2 pith:5ITMCUQD submitted 2025-01-06 astro-ph.IM gr-qc

Nir Guttman , Paul D. Lasky , Eric Thrane This is my paper · ORCID
classification astro-ph.IMgr-qc
keywords gravitational-wavenoisetransdimensionalBayesianinferencepowerspectraldensityestimationBilbyshapeletsLorentzianlinesparameterLIGO/Virgo
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces tPowerBilby, a transdimensional Bayesian model that characterizes gravitational-wave detector noise as a combination of power laws for broadband features, damped Lorentzians for narrowband lines, and shapelet basis functions for features in between. It claims this model fits the LIGO and Virgo amplitude spectral densities better than the empirical Welch estimate and the BayesLine-based noise curves used in the GWTC-3 catalog. Applying the model to GW150914, GW190521, and GW190929, the authors find that reweighting existing posterior samples shifts some 90% credible-interval boundaries by up to 7% and some median values by up to 10%. If these shifts are real, noise misspecification is a leading source of systematic error in gravitational-wave source inference rather than a subdominant one.

What carries the argument

The load-bearing object is the transdimensional noise model in Eq. (2.3), whose amplitude spectral density is $\sigma(f) = \max[\sigma_{\rm BB}(f, \Lambda_{\rm BB}), \sigma_{\rm NB}(f, \Lambda_{\rm NB})]$. Broadband noise is a sum of power laws plus shapelets; narrowband noise is a sum of exponentially damped Lorentzians plus shapelets, where shapelets are Hermite-polynomial basis functions that capture features neither power laws nor Lorentzians describe. The number of power laws $N_{\rm PL}$, the number of lines $N_{\rm line}$, and the shapelet degrees $\deg$ are discrete parameters sampled transdimensionally, so the model adapts its own complexity. The max operation, a frequency-dependent line prior built from adjacent data, and a six-subband sampling scheme keep the fit tractable, while a pre/post mixture likelihood in Eq. (3.2) absorbs non-stationarity.

What would settle it

Run the same pre/post mixture and importance-sampling analysis on an injected signal buried in data with a known true PSD and with artificially correlated frequency bins; if the recovered 90% credible intervals shift by up to 7% relative to the true-PSD analysis, the shift is a real noise-model effect, while if they remain stable, the shifts seen in GW150914 and the other events could be artifacts of the Whittle approximation.

Watch

Extended reading notes

Core claim

The central claim is that a transdimensional noise model—one that lets the number of power laws, Lorentzians, and shapelets float as free parameters—describes the LIGO and Virgo amplitude spectral density more accurately than the fixed empirical curves used in published analyses, and that this choice of noise model changes some astrophysical parameter estimates. The model builds the total noise ASD as $\sigma(f) = \max[\sigma_{\rm BB}(f), \sigma_{\rm NB}(f)]$, so broadband and narrowband fits decouple, and it samples the noise parameters with the Dynesty nested sampler through Bilby. The evidence is a series of $\Delta\ln L$ comparisons showing tPowerBilby fits the data better than Welch and GWTC-3 curves, Kolmogorov-Smirnov tests of whitened data, and an injection study in which injected parameters are recovered. The shifts are not uniform: the paper reports up to 7% changes in the 90% credible-interval boundaries and up to 10% shifts in medians for specific parameters of specific events.

Load-bearing premise

The model's likelihood treats noise as Gaussian and stationary with uncorrelated frequency bins; the paper concedes that real detector noise has correlations and non-stationarity that can produce systematic errors comparable to the very effects it measures.

Editorial extensions

If this is right

  • If the central claim is right, published GWTC-3 posterior samples for GW150914, GW190521, and GW190929 carry a noise-modeling systematic of up to 7% in some 90% credible-interval widths, comparable to calibration and waveform systematics.
  • Using tPowerBilby noise curves from before and after an event, combined through the mixture model, reduces non-stationarity losses, making the method suitable for routine off-source noise estimation.
  • Importance-sampling efficiencies of 39-55% mean existing posterior samples can be reweighted, so a systematic re-analysis of catalog events is feasible without rerunning expensive parameter estimation.
  • Because the model returns posterior samples over the number of lines and shapelets, it quantifies noise-model uncertainty rather than providing only a single noise curve.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension the paper leaves implicit: the same importance-sampling weights can be applied to the full set of GWTC-3 posterior samples without resampling, so a catalog-wide map of noise-modeling systematic error could be produced at modest computational cost.
  • Because the Whittle likelihood ignores off-diagonal frequency correlations, the reported shifts should be tested against a likelihood that includes a full noise covariance matrix; the paper's own footnote says those correlations can produce errors comparable to the effects being measured.
  • Using tPowerBilby's fitted curves as a prior for a joint on-source noise-signal run, rather than as an off-source reweighting, would directly check whether the 7% shifts persist; the paper lists this as future work.
  • The line and shapelet amplitude bounds are set from adjacent data with fixed safety factors of 3.5 and 3.85; testing those thresholds across many observatories and epochs would show whether the improved fit is robust or partly tuned to the examples chosen.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript introduces tPowerBilby, a transdimensional Bayesian model for gravitational-wave detector noise, implemented within the Bilby framework. The noise amplitude spectral density is modelled as a maximum of broadband components (power laws plus broadband shapelets) and narrowband components (Lorentzians with damped tails plus narrowband shapelets), with transdimensional priors on the number of components. The method is applied to three GWTC-3 events (GW150914, GW190521, GW190929), where the authors report improved fits relative to the GWTC-3 BayesLine noise curves and to Welch estimates, and they use importance sampling to reweight posterior samples, finding shifts of up to about 7% in 90% credible-interval widths and up to about 10% in median values for some astrophysical parameters. An injection study in Appendix D and an open-source software package are included.

Significance. If the central claims hold, the paper offers a useful, publicly available tool for noise spectral estimation with transdimensional sampling, and it quantifies a potentially important systematic error in gravitational-wave parameter estimation. The strengths of the paper include the open-source implementation, the explicit discussion of limitations (notably the footnote in Sec. I about the diagonal-Whittle assumption), and the independent injection study in Appendix D, which checks parameter recovery and reports a high reweighting efficiency. The main scientific payoff, however, rests on in-sample likelihood comparisons and on the assumed form of the noise likelihood; the reported improvements and credible-interval shifts need additional out-of-sample or assumption-robust validation before they can be interpreted as measured systematics.

major comments (4)
  1. [Sec. III A, Eq. (3.1)] The central claim of a 'significantly improved fit' is supported by Delta ln L values that compare the maximum-likelihood tPowerBilby curve, fit to the same off-source data on which the likelihood is evaluated, with the GWTC-3 median BayesLine curve. A maximum-likelihood curve from a flexible transdimensional model will almost always achieve a higher likelihood on its own training data, so the reported Delta ln L conflates genuine model quality with in-sample overfitting. Please add a held-out validation: fit tPowerBilby on one off-source segment and evaluate the likelihood on an independent segment, or use posterior predictive checks on data not used in the fit, and compare both models on identical off-source data. This is load-bearing because the abstract's 'significantly improved fit' claim is based on this comparison.
  2. [Sec. I, footnote 1, and Eq. (2.1)] The paper acknowledges in the footnote to Sec. I that the diagonal-Whittle assumption is not exactly true and that 'the resulting error can produce systematic errors comparable to the effects we study here.' Since the headline 7% credible-interval shifts are the main scientific payoff, the possibility that these shifts are dominated by correlated-frequency-bin systematics is a load-bearing concern. Please quantify the impact of this assumption: for example, estimate the correlation of whitened residuals in adjacent bins, recompute the likelihood gains with coarser frequency binning or with spectral lines notched, and demonstrate that tPowerBilby and the comparison models recover a known injected PSD before interpreting the Delta ln L values as evidence of a better noise model.
  3. [Sec. III B, Eq. (3.2), and Table III] Several important hyperparameters are fixed by hand without a sensitivity study: the mixture weight lambda = 0.5, the line-tail damping rate tau = 5.2, the line-detection threshold 3.5, the shapelet amplitude cap factor 3.85, and the high-quality data cutoff 5. The reported likelihood gains and the astrophysical shifts could depend on these choices. Please provide a sensitivity analysis that varies lambda and the thresholds and reports whether the Delta ln L values and the credible-interval shifts persist, or justify the choices with a cross-validated selection procedure rather than 'determined by experimentation' in Sec. II E 2. Without this, the robustness of the 7% shifts is not established.
  4. [Sec. III C and Table IV] The reweighting comparison in Eq. (3.4) uses tPowerBilby noise parameters estimated from off-source data and evaluates the likelihood on on-source data, while the GWTC-3 comparison curve is a point estimate (the median) from on-source BayesLine fits. The reported ln B values therefore do not represent a controlled model comparison: differences can arise from off-source versus on-source non-stationarity, from point-estimate versus marginalized noise, or from model flexibility. Please compare both approaches using the same data segments and, where possible, use BayesLine posterior draws rather than the median curve so that the comparison is between two marginalized noise models.
minor comments (5)
  1. [Fig. 3 caption] The caption notes that the GWTC-3 curve is available only up to 225 Hz for GW190521; please state explicitly how Eq. (3.1) and the Delta ln L calculation handle different frequency ranges for the three events.
  2. [Sec. II E 3] There is a typo, 'shaplelet' for 'shapelet', in the text introducing the shapelet prior.
  3. [Eq. (2.6)] The damping parameter tau is described as a 'characteristic decay scale', but the units in Table I are Hz^-1; please clarify the interpretation and the functional form of the exponential decay in Eq. (2.6).
  4. [Sec. III B] The text says lambda 'can be fit as a free parameter' but the analysis fixes lambda = 0.5; a brief comment on whether a free lambda changes any of the reported results would be useful.
  5. [Table IV] The ln B values are quoted without uncertainties; please report Monte Carlo errors from the importance-sampling estimate, especially because the values for GW150914 and GW190929 are both exactly 20.

Circularity Check

1 steps flagged · score 4.0 of 10

The 'significantly improved fit' claim rests on an in-sample maximum-likelihood comparison, but the astrophysical shifts are anchored by an independent injection study, so circularity is partial.

  1. fitted input called prediction [Sec. III A (Eq. 3.1); Sec. II F; Sec. III C (Table IV)]
    "We measure the difference in natural log likelihood to compare our preferred model maximum-likelihood fit to the fit from GWTC-3: ∆ lnL = ln LtPowerBilby − ln LGWTC. ... The σGWTC fit was obtained using BayesLine with on-source data and estimated from the median value for each frequency bin’s inferred posterior distribution."

    The score used to claim superiority is the same objective function that was maximized to produce the tPowerBilby curve. Eq. (3.1) evaluates ln L_tPowerBilby at the maximum-likelihood point estimate of a flexible transdimensional model fitted to the displayed data, while ln L_GWTC is evaluated at a posterior-median curve from a different model fitted to on-source data. A maximum-likelihood estimate always has likelihood at least as high as any other fixed curve on the training data, so a positive ∆lnL is guaranteed by construction regardless of which model is closer to the true noise. The line-location prior is built from the same data (Appendix B1), so the 'notable gains associated with spectral lines' are pre-wired rather than out-of-sample.

full rationale

The paper's core derivation—noise model Eq. (2.3), sampling procedure Sec. II F, and importance reweighting Eq. (3.4)—is not definitionally circular: the tPowerBilby noise parameters are estimated from off-source data and then used to reweight existing GWTC-3 posterior samples, so the 7% credible-interval shifts are not fitted to the target parameters. The injection study in Appendix D provides an external falsifiable check: injected parameters are recovered with ln B ≈ 27 and efficiency ≈ 92%. The main circularity is confined to the fit-comparison claim: Eq. (3.1) and Table IV compare the model's own maximum-likelihood curve on the training data against a posterior-median curve from an inequivalent baseline, making positive ∆lnL statistically forced. The footnote in Sec. I concedes that the diagonal-Whittle assumption can produce 'systematic errors comparable to the effects we study here,' which is a correctness caveat rather than a circular step. Self-citations (e.g., [4], [9], [25]) are used for standard methods and caveats, not as load-bearing uniqueness arguments, and no ansatz is smuggled in solely via self-citation. On balance, the central inference result has independent empirical content, so the paper is only partially circular.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The ledger lists hand-chosen constants and background assumptions the method depends on. No invented entities are introduced; all basis functions are standard. The dominant burden is the Whittle-likelihood assumption and the many thresholds set by experimentation.

free parameters (8)
  • Fixed line-tail damping rate tau = 5.2 Hz^-1
    Set by experimentation (Sec. II E2, Table II); affects Lorentzian tail shape.
  • Prior mean and width for line damping start zeta = mean=2.7, sigma=1.1
    Chosen by experimentation (Sec. II E2); controls how quickly Lorentzian tails are truncated.
  • Line detection threshold = 3.5 x broadband median
    Ad hoc threshold in Appendix B1 for constructing the line-location prior.
  • Shapelet amplitude cap = 3.85 x broadband median = 1.1 x 3.5
    Ad hoc safety margin in Appendix B2 preventing shapelets from fitting lines too aggressively.
  • High-quality data cutoff = 5 x fitted broadband sigma
    Factor chosen to balance rejecting noisy bins and retaining signal (Sec. II G, Appendix B3); low-quality bins are excluded from fit metrics.
  • Mixture weight lambda = 0.5
    Fiducial value adopted in Sec. III B rather than fitted; weights pre/post noise estimates.
  • Number of shapelet components NBBS/NBS = 4
    Fixed because two-level transdimensional sampling is not supported by the Bilby extension (Sec. II E3).
  • Segmentation parameters = 30 Hz minimum gap, 100 Hz separation
    Defaults in Appendix B4 that determine sub-band boundaries.
assumptions (5)
  • domain assumption Noise is Gaussian, stationary, and independent across frequency bins, giving the Whittle likelihood (Eq. 2.1).
    Invoked in Sec. II A; the paper's footnote in Sec. I admits correlated frequency bins can cause systematics comparable to the effect under study.
  • domain assumption Off-source data before or after an event has the same noise PSD as the on-source segment.
    Used throughout to fit sigma(f) on adjacent data and transfer it to the event (Sec. I, III A).
  • domain assumption The true PSD lies in the model family max(broadband sum, narrowband sum) with power laws, damped Lorentzians, and shapelets.
    Central modeling assumption in Sec. II; no proof that this family can represent real detector noise without bias.
  • domain assumption The BayesLine posterior used for importance sampling is sufficiently close to the tPowerBilby posterior for reweighting.
    Sec. III B relies on reweighting efficiency of at least 2%; measured efficiencies of 39-55% support it for the three events, but it is not guaranteed generally.
  • domain assumption Dynesty nested sampling converges for the transdimensional posteriors.
    The paper assumes the sampler produces reliable posterior samples, but does not demonstrate convergence diagnostics.

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Cite this review

Pith. "Pith review of Modelling noise in gravitational-wave observatories with transdimensional models." pith.science (2026). https://pith.science/paper/5ITMCUQD

@misc{pith2026250103285,
  author       = {Pith},
  title        = {Pith review of: Modelling noise in gravitational-wave observatories with transdimensional models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ITMCUQD}},
  note         = {Machine review of arXiv:2501.03285}
}
abstract

Modelling noise in gravitational-wave observatories is crucial for accurately inferring the properties of gravitational-wave sources. We introduce a transdimensional Bayesian approach to characterise the noise in ground-based gravitational-wave observatories using the Bayesian inference software $\texttt{Bilby}$. The algorithm models broadband noise with a combination of power laws; narrowband features with Lorentzians; and shapelets to capture any additional features in the data. We show that our noise model provides a significantly improved fit of the LIGO and Virgo noise amplitude spectral densities compared to currently available noise fits obtained with on-source data segments. We perform astrophysical inference on well-known events in the third Gravitational-Wave Transient Catalog using our noise model and observe shifts of up to $7\%$ in the $90\%$ boundaries of credible intervals for some parameters. We discuss plans to deploy this framework systematically for gravitational-wave inference along with possible areas of improvement.

Figures

Figures reproduced from arXiv: 2501.03285 by the authors.

Figure 1
Figure 1. FIG. 1. A typical noise curve for the LIGO Livingston ob [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Estimates for the noise for the Livingston interferometer in the vicinity of the gravitational-wave signal [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Estimates for the noise for the Livingston interferometer in the vicinity of the gravitational-wave signal [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Marginalized posterior distribution for the broadband noise parameters for the Livingston interferometer following [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Distribution of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Frequency-domain whitened data preceding the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Quality of fit spectrum. The plot contains two vertical axes with a common horizontal axis. On the left vertical axis, [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Marginalized posterior distributions for [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. As with Fig. 8, but for the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. As with Fig. 8, but for the [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Quality of fit spectrum. The plot contains two vertical axes with a common horizontal axis. On the left vertical axis, [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Marginalized posterior distributions for the injected signal, with parameters listed in Tab. V, showing the masses [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]

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Reference graph

Works this paper leans on

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