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REVIEW 4 major objections 4 minor 64 references

Statistical biases in parametrized searches for gravitational-wave polarizations

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

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Pith's one-line read Selecting loud gravitational-wave events biases scalar-mode tests of gravity.

desk verdict Useful caution about prior mismatch in scalar-tensor polarization searches, but the selection-effect framing overreaches: the bias is shown for loud injections at fixed distance, not for an actual detection selection. read the letter →

arxiv 2501.16788 v3 pith:MVAAWW5F submitted 2025-01-28 gr-qc

Hayato Imafuku , Hiroki Takeda , Atsushi Nishizawa , Daiki Watarai , Kipp Cannon This is my paper · ORCID
classification gr-qc MSC 83C3562F15 PACS 04.30.-w95.85.Sz
keywords gravitationalwavesscalar-tensortheorygravitational-wavepolarizationsparameterestimationbiasselectioneffectsBayesianinferenceluminositydistance-inclinationdegeneracyscalardipolemode
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

This paper argues that choosing only loud, high-signal-to-noise gravitational-wave events for parameter estimation can bias tests of general relativity that search for scalar polarization modes. Using injection studies with a parametrized scalar-tensor inspiral waveform, it shows that when a scalar dipole component is truly present, standard Bayesian inference with a uniform-in-comoving-volume distance prior overestimates the scalar dipole amplitude $A_{b1}$. The mechanism is that the prior pulls the inferred inclination toward face-on values ($\cos\iota\sim 1$), suppressing $\sin\iota$, which the amplitude estimator compensates by inflating $A_{b1}$. The bias disappears when the true scalar amplitude is zero, so the analysis does not create a false scalar detection from noise alone; the same effect is expected for the scalar quadrupole mode, though generic degeneracies make that measurement too noisy to show a clean bias.

What carries the argument

The central object is the parametrized scalar-tensor inspiral waveform with amplitude parameters $A_{b1}$ (dipole) and $A_{b2}$ (quadrupole), together with the known luminosity-distance/inclination degeneracy and the uniform-in-comoving-volume prior $p(d_L)\propto d_L^2$. For pure tensor signals the posterior $p(\cos\iota)\propto\cos^3\iota$ favors $\cos\iota\sim1$, while for pure scalar dipole signals $p(\sin\iota)\propto\sin^3\iota$ favors $\cos\iota\sim0$. In the mixed model, tensor dominance biases the inferred inclination toward face-on, suppressing $\sin\iota$, and the scalar amplitude estimator compensates by overestimating $A_{b1}$.

What would settle it

Re-run the Tensor+Scalar(dipole) injections with a distance prior conditioned on the selection, for example a prior sharply peaked at the injected distance or a truncated signal-to-noise-ratio-based selection prior, and check whether the median recovered $A_{b1}$ returns to the injected value. If the overestimation disappears, the bias is a prior-mismatch effect as claimed; if it persists, the mechanism is different.

Watch

Extended reading notes

Core claim

The paper claims that the amplitude of scalar dipole radiation is overestimated whenever its true value is nonzero and the event is selected as loud, except when the inclination is exactly $\pi/2$. This overestimation arises because the tensor-mode-dominated inference, combined with a uniform-in-comoving-volume luminosity-distance prior, drives the posterior of $\cos\iota$ toward $1$, underestimating $\sin\iota$. Since the scalar dipole waveform amplitude is proportional to $A_{b1}\sin\iota$, the inference compensates by raising $A_{b1}$. When $A_{b1}=0$, no false deviation occurs, so the bias is conditional on a real scalar component existing. The same qualitative mechanism is argued to hold for the Tensor+Scalar(quadrupole) model, but the scalar quadrupole amplitude is too poorly constrained by the data for the bias to dominate over statistical error.

Load-bearing premise

The injections place all loud events at a fixed distance of 204 Mpc with signal-to-noise ratios between 20 and 100, while the prior assumes a uniform comoving-volume distribution, and the analysis applies no actual detection threshold or selection function, so the reported bias is the consequence of prior mismatch for a loud event rather than a demonstrated selection effect.

Editorial extensions

If this is right

  • A single loud gravitational-wave event analyzed without modeling the selection will tend to overreport the scalar dipole amplitude whenever a real scalar dipole component is present.
  • The bias is absent when the true scalar amplitude is zero, meaning the test does not manufacture false scalar detections from prior mismatch alone.
  • The inclination angle is recovered more accurately as the scalar amplitude increases, because the scalar mode's distinct angular pattern pulls the posterior back toward the true inclination.
  • For the scalar quadrupole model, the amplitude measurement is largely uninformative because tensor and scalar quadrupole share the same phase evolution, so statistical error exceeds the selection bias.
  • Multi-event statistical searches or priors that explicitly model the selection process are proposed as ways to remove the bias.

Reading between the lines

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

  • The same prior-mismatch mechanism should affect any amplitude parameter that is correlated with inclination and luminosity distance, so other parametrized post-Einsteinian searches should be checked for analogous biases.
  • If real catalogs select events by signal-to-noise ratio, current upper limits on scalar dipole radiation derived from individual loud events may be systematically shifted in the direction of overestimating the scalar amplitude.
  • A hierarchical population analysis that jointly models the detection probability and the source distribution would provide a direct test of whether this bias persists in actual observational data.
  • Third-generation detectors with signal-to-noise ratios roughly ten times higher may suppress the bias because the likelihood dominates the prior, but the threshold depends on source orientation and detector network.
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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 / 4 minor

Summary. The paper studies how selecting loud gravitational-wave events can bias parametrized searches for scalar-tensor polarizations. The authors construct a parametrized inspiral waveform containing tensor modes plus scalar dipole and quadrupole modes, with non-GR amplitude parameters Ab1 and Ab2. Using Bilby with nested sampling, they perform injection-recovery runs: pure tensor, pure scalar dipole, and mixed Tensor+Scalar(dipole) and Tensor+Scalar(quadrupole) injections, all at a fixed luminosity distance of 204 Mpc with SNRs in the range 20--100, while adopting a prior uniform in comoving volume. They report that the pure tensor mode favors cos iota ~ 1 while the pure scalar dipole mode favors cos iota ~ 0, and that in the Tensor+Scalar(dipole) model the scalar dipole amplitude Ab1 is overestimated when the true Ab1 is nonzero, except at iota = pi/2, with no false deviation when Ab1 = 0. The quadrupole amplitude is found to be poorly constrained. The paper concludes that event selection can bias scalar-mode amplitude estimation unless selection effects are properly modeled.

Significance. If the central claim is correct, the paper identifies a practically important effect for current and future tests of general relativity: using a volume-weighted distance prior on loud, selected events can bias the inferred scalar dipole amplitude, potentially creating false evidence for non-GR polarizations or exaggerating real ones. The physical mechanism is clearly explained and the pure-polarization inclination bias is supported by a simple analytic scaling argument. The paper also has positive reproducibility features: it uses standard tools (Bilby, dynamic nested sampling, LALSuite TaylorF2), states the sampler settings, and gives explicit injection parameters. The main caveats are that the selection process is not actually simulated, the mixed-polarization statistical evidence is based on only three injections per configuration without significance tests, and the quadrupole bias is asserted rather than demonstrated. These issues do not invalidate the qualitative mechanism but they do limit the strength of the quantitative claims, and they need to be addressed before the paper can be accepted.

major comments (4)
  1. [Section III, Sec. III and IV] The paper's central claim is that event selection biases the scalar dipole amplitude, but no selection function or detection threshold is actually implemented. All injections are placed at a fixed distance dL = 204 Mpc, giving SNRs of 20-100, and are then all analyzed; the paper itself states in Sec. III that "the distributions of these 50 GW signals do not follow the prior distribution shown in Table II." The observed bias is therefore a prior-misspecification effect for loud events, not a demonstrated selection effect, since conditioning on detection would modify the prior by P(det|theta), which is not included. This is load-bearing because the abstract and Sec. V attribute the bias specifically to event selection. The authors should either implement an explicit selection function (e.g., a network SNR threshold applied to a population of injections drawn from the prior) or carefully reframe the results as a prior-mismatch bias for loud events and justify why this captures the selection effect of interest.
  2. [Section IV B, Figs. 2, 4, 5] The mixed-polarization overestimation claim for Ab1 is supported by only three injection realizations per parameter setting, with no significance test or quantitative measure of bias. The figures show medians and 90% credible intervals, but the reader cannot tell how many of the three estimates exceed the true value, whether the posterior mass above the injected value is significant, or how often the 90% intervals exclude the truth. To support the claim that Ab1 is systematically overestimated, the authors should either increase the number of noise realizations or report a per-injection summary statistic such as the fraction of posterior samples above the injected value, and ideally a statement about the distribution of posterior medians across realizations. This is particularly important at iota = pi/2, where the posterior is bimodal (Fig. 3) and a median may be a poor summary.
  3. [Abstract and Sec. V] The abstract states that the quadrupole bias "is expected to occur also for the Tensor+Scalar(quadrupole) model," but Sec. IV B concludes that the scalar quadrupole amplitude results are "uninformative" and that the errors are constrained by the prior range [-1,1]. The paper does not demonstrate any bias in Ab2, so this expected claim is not supported by the presented simulations. Either add a simulation or analytic argument establishing the quadrupole bias, or soften the abstract and conclusions to state that the quadrupole amplitude is too poorly constrained to detect the bias.
  4. [Section IV A, Eqs. (4.1) and (4.2)] The analytic results p(cos iota) proportional to cos^3 iota and p(sin iota) proportional to sin^3 iota are central to the interpretation, but they are stated with a very brief derivation. The derivation should be written out more explicitly, including the assumption of an exactly degenerate likelihood in the amplitude combination and the marginalization over dL with the volume prior. This would also clarify the conditions under which the formula applies, since the full posterior with a three-detector network and finite SNR will only approximately follow this scaling.
minor comments (4)
  1. [Throughout] There are several typographical and formatting issues, including inconsistent spacing in "L VK" (used for the LIGO-Virgo-KAGRA collaboration) and the notation "rad-dec set" in Appendix A, which should be "ra-dec set." A careful proofread for these minor errors is recommended.
  2. [Fig. 2 caption] The caption says the panels run "from top right to bottom left," but the standard reading (and the layout described in the text) is from top left to bottom right. Please correct the caption.
  3. [Reference [38]] Reference [38] is listed as "T. Bayes, Philosophical Transactions of the Royal Society of London, 370 (1973)"; the original paper by Bayes was published in 1763, not 1973. The reference should be corrected.
  4. [Section III] The text says that "p(d|theta, M) is the likelihood" in Eq. (3.1), but Eq. (3.4) then introduces the likelihood as proportional to exp(-(1/2) sum ...). This is standard, but the notation could be harmonized so that the likelihood is not defined twice in different forms without comment.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bias result is a controlled injection-recovery finding, not a derivation that reduces to its inputs.

full rationale

The paper is an injection-recovery simulation study rather than a claim to derive a first-principles prediction from the model. The central finding—that the scalar dipole amplitude Ab1 is biased upward when its true value is nonzero, under the stated volume-weighted distance prior—is an output of Bayesian inference performed with Bilby and LALSuite, conditional on the explicitly stated waveform, priors, and injection distribution. The analytic relations p(cos i) ∝ cos^3 i and p(sin i) ∝ sin^3 i are derived from the assumed prior and amplitude scalings, not fitted from the injections. The waveform parametrization is adopted transparently from the authors' earlier works [22,23]; this is a self-citation, but it is not load-bearing for the statistical bias claim, which would hold for any model with tensor amplitude ∝ cos i/dL and scalar dipole amplitude ∝ Ab1 sin i/dL. No fitted parameter is relabeled as a prediction, and no equation is equivalent to its own input by construction. The absence of an explicit detection-threshold selection function is a possible limitation of the study's external validity, but it is a correctness concern rather than a circularity; the paper explicitly acknowledges that the injected signals do not follow the prior. The derivation chain is self-contained for the purpose of demonstrating the bias mechanism.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the imported scalar-tensor waveform, the prior choices, and the way selection is represented. No new physical entities or fitted constants are introduced, but the demonstration depends on several hand-chosen injection and prior settings.

free parameters (6)
  • Injection luminosity distance = 204 Mpc
    Chosen injection distance producing SNR 20-100; the mismatch between this fixed distance and the uniform-in-comoving-volume prior is what generates the reported bias.
  • Injected scalar amplitude grid = 0, 0.1, 0.3, 0.5 for Ab1; 0, plus or minus 0.1, 0.3, 0.5 for Ab2
    Chosen set of injected non-GR amplitudes; the central claim is demonstrated only at these values, not across a continuous range.
  • Prior range for luminosity distance = [10, 1500] Mpc, uniform in comoving volume
    This prior choice drives the cos iota bias through p(cos iota) proportional to cos^3 iota; a different distance prior would change or remove the bias.
  • Prior range for non-GR parameters = [-1, 1] for Ab1, Ab2, tilde Ab1, tilde Ab2
    Uniform priors on the scalar amplitudes; the width encodes the assumption that scalar amplitudes are smaller than tensor amplitudes and affects the posterior spread.
  • Injection sky location = alpha = 0.833 rad, delta = -0.784 rad
    A single sky location is used for the mixed-polarization injections; Appendix A argues it is typical, but the main figures depend on this choice.
  • Injected masses = 15 and 10 solar masses
    Chosen to set the inspiral frequency band and SNR; the mass scale affects the Fisher information and therefore the magnitude of the bias.
assumptions (6)
  • domain assumption The parametrized scalar-tensor waveform of Eqs. (2.8)-(2.11) correctly describes gravitational waves for the purpose of injection recovery.
    The waveform is imported from Refs. [22,23] without modification; if it is inaccurate, the estimated biases do not reflect real analyses.
  • domain assumption Detector noise is stationary and Gaussian, and the O4 design PSDs approximate actual detector performance.
    The likelihood in Eq. (3.4) and all injections assume stationary Gaussian noise; real noise non-stationarities are ignored.
  • ad hoc to paper The selection effect is adequately represented by injecting loud signals at fixed distance rather than applying an explicit detection threshold to a population.
    No detection statistic is simulated; the selected ensemble is created by construction, so the paper demonstrates prior-mismatch bias rather than selection bias in the usual sense.
  • domain assumption The prior for luminosity distance is uniform in comoving volume over [10,1500] Mpc.
    This prior, combined with fixed-distance injections, produces the cos iota approximately 1 preference that drives the Ab1 bias.
  • domain assumption Inclination and distance are strongly correlated for the three-detector network considered, so p(cos iota) proportional to cos^3 iota applies.
    Derived in Sec. IV A using the dL-cos iota degeneracy; relies on the detector network and the absence of higher-order modes.
  • domain assumption The inspiral-only, aligned-spin, no-higher-modes waveform is sufficient to expose the selection bias.
    The authors acknowledge that higher modes and spins would break degeneracies and change the bias; the quantitative results are contingent on this restriction.

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Cite this review

Pith. "Pith review of Statistical biases in parametrized searches for gravitational-wave polarizations." pith.science (2026). https://pith.science/paper/MVAAWW5F

@misc{pith2026250116788,
  author       = {Pith},
  title        = {Pith review of: Statistical biases in parametrized searches for gravitational-wave polarizations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MVAAWW5F}},
  note         = {Machine review of arXiv:2501.16788}
}
read the original abstract

In tests of gravity using gravitational waves (GWs), GW events analyzed are often selected based on specific criteria, particularly the signal-to-noise ratio. However, such event selection can introduce bias into parameter estimation unless the selection effect is appropriately taken into account in the analysis. In this paper, we investigate how event selection with certain prior information affects parameter inference within the scalar-tensor polarization framework, focusing on the measurement of the scalar mode amplitude parameters. We find that for the Tensor+Scalar(dipole) model, the amplitude of the scalar dipole radiation is overestimated when its true value is nonzero while there is no false deviation in the absence of the scalar mode. The same bias is expected to occur also for the Tensor+Scalar(quadrupole) model. However, the error typically exceeds the bias as the scalar quadrupole mode is difficult to be distinguished from the tensor mode.

Figures

Figures reproduced from arXiv: 2501.16788 by the authors.

Figure 1
Figure 1. FIG. 1: The histograms of the inclination recovery for the case of pure tensor mode (blue) and pure scalar dipole [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The medians and the error bars of the inclination angle and the amplitude of the scalar dipole mode. Each [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The posterior probability distributions of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The medians and the error bars of the inclination angle and the amplitude of the scalar quadrupole mode [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The medians and the error bars of the inclination angle and the amplitude of the scalar quadrupole mode [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: The dependence of the deviation between the median and the true value of cos [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Reference graph

Works this paper leans on

64 extracted references · 6 canonical work pages

  1. [1]

    C. M. Will, Living Rev. Rel. 17, 4 (2014), arXiv:1403.7377 [gr-qc]

    arXiv 2014

  2. [2]

    C. M. Will, Theory and Experiment in Gravitational Physics, 2nd ed. (Cambridge University Press, 2018)

    2018

  3. [3]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc]

    arXiv 2016

  4. [4]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 116, 221101 (2016), [Erratum: Phys.Rev.Lett. 121, 129902 (2018)], arXiv:1602.03841 [gr-qc]

    arXiv 2016

  5. [5]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. 11 0 10 20 30 40 50 rad-dec set −0.25 −0.20 −0.15 −0.10 −0.05 0.00 0.05 cos ιmedian − cos ιtrue Tensor, ι= π/6 median of deviation = 0 .015 no deviation 0 10 20 30 40 50 rad-dec set −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20 cos ιmedian − cos ιtrue Tensor, ι= π/4 median of deviation = 0 .163 n...

    arXiv 2019

  6. [6]

    Abbott et al

    R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 11, 021053 (2021), arXiv:2010.14527 [gr-qc]

    arXiv 2021

  7. [7]

    Abbott et al

    R. Abbott et al. (KAGRA, VIRGO, LIGO Scientific), Phys. Rev. X 13, 041039 (2023), arXiv:2111.03606 [gr- qc]

    arXiv 2023

  8. [8]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 100, 104036 (2019), arXiv:1903.04467 [gr-qc]

    arXiv 2019

Show all 64 references
  1. [9]

    Abbott et al

    R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 103, 122002 (2021), arXiv:2010.14529 [gr-qc]

    2021 arXiv

  2. [10]

    Abbott et al

    R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA), (2021), arXiv:2112.06861 [gr-qc]

    2021 arXiv

  3. [11]

    D. M. Eardley, D. L. Lee, A. P. Lightman, R. V. Wagoner, and C. M. Will, Phys. Rev. Lett. 30, 884 (1973)

    1973

  4. [12]

    D. M. Eardley, D. L. Lee, and A. P. Lightman, Phys. Rev. D 8, 3308 (1973)

    1973

  5. [13]

    Berti, K

    E. Berti, K. Yagi, and N. Yunes, Gen. Rel. Grav. 50, 46 (2018), arXiv:1801.03208 [gr-qc]

    2018 arXiv

  6. [14]

    Tahura and K

    S. Tahura and K. Yagi, Phys. Rev. D 98, 084042 (2018), [Erratum: Phys.Rev.D 101, 109902 (2020)], arXiv:1809.00259 [gr-qc]

    2018 arXiv

  7. [15]

    Chatziioannou, N

    K. Chatziioannou, N. Yunes, and N. Cornish, Phys. Rev. D 86, 022004 (2012), [Erratum: Phys.Rev.D 95, 129901 (2017)], arXiv:1204.2585 [gr-qc]

    2012 arXiv

  8. [16]

    P. T. H. Pang, R. K. L. Lo, I. C. F. Wong, T. G. F. Li, and C. Van Den Broeck, Phys. Rev. D 101, 104055 (2020), arXiv:2003.07375 [gr-qc]

    2020 arXiv

  9. [17]

    Hagihara, N

    Y. Hagihara, N. Era, D. Iikawa, A. Nishizawa, and H. Asada, Phys. Rev. D 100, 064010 (2019), arXiv:1904.02300 [gr-qc]

    2019 arXiv

  10. [18]

    Chatziioannou, M

    K. Chatziioannou, M. Isi, C.-J. Haster, and T. B. Litten- berg, Phys. Rev. D 104, 044005 (2021), arXiv:2105.01521 12 [gr-qc]

    2021 arXiv

  11. [19]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 119, 141101 (2017), arXiv:1709.09660 [gr-qc]

    2017 arXiv

  12. [20]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 123, 011102 (2019), arXiv:1811.00364 [gr-qc]

    2019 arXiv

  13. [21]

    Takeda, S

    H. Takeda, S. Morisaki, and A. Nishizawa, Phys. Rev. D 103, 064037 (2021), arXiv:2010.14538 [gr-qc]

    2021 arXiv

  14. [22]

    Takeda, S

    H. Takeda, S. Morisaki, and A. Nishizawa, Phys. Rev. D 105, 084019 (2022), arXiv:2105.00253 [gr-qc]

    2022 arXiv

  15. [23]

    Takeda, S

    H. Takeda, S. Tsujikawa, and A. Nishizawa, Phys. Rev. D 109, 104072 (2024), arXiv:2311.09281 [gr-qc]

    2024 arXiv

  16. [24]

    Takeda, Y

    H. Takeda, Y. Manita, H. Omiya, and T. Tanaka, PTEP 2023, 073E01 (2023), arXiv:2304.14430 [gr-qc]

    2023 arXiv

  17. [25]

    Cutler and E

    C. Cutler and E. E. Flanagan, Phys. Rev. D 49, 2658 (1994), arXiv:gr-qc/9402014

    1994 arXiv

  18. [26]

    Nissanke, D

    S. Nissanke, D. E. Holz, S. A. Hughes, N. Dalal, and J. L. Sievers, Astrophys. J. 725, 496 (2010), arXiv:0904.1017 [astro-ph.CO]

    2010 arXiv

  19. [27]

    S. A. Usman, J. C. Mills, and S. Fairhurst, Astrophys. J. 877, 82 (2019), arXiv:1809.10727 [gr-qc]

    2019 arXiv

  20. [28]

    Veitch, I

    J. Veitch, I. Mandel, B. Aylott, B. Farr, V. Raymond, C. Rodriguez, M. van der Sluys, V. Kalogera, and A. Vec- chio, Phys. Rev. D 85, 104045 (2012), arXiv:1201.1195 [astro-ph.HE]

    2012 arXiv

  21. [29]

    Narikawa, M

    T. Narikawa, M. Kaneyama, and H. Tagoshi, Phys. Rev. D 96, 084067 (2017), arXiv:1705.04008 [gr-qc]

    2017 arXiv

  22. [30]

    Takeda, A

    H. Takeda, A. Nishizawa, Y. Michimura, K. Nagano, K. Komori, M. Ando, and K. Hayama, Phys. Rev. D 98, 022008 (2018), arXiv:1806.02182 [gr-qc]

    2018 arXiv

  23. [31]

    Maggiore, Gravitational Waves

    M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments (Oxford University Press, 2007)

    2007

  24. [32]

    S. Droz, D. J. Knapp, E. Poisson, and B. J. Owen, Phys. Rev. D 59, 124016 (1999), arXiv:gr-qc/9901076

    1999 arXiv

  25. [33]

    Yunes, K

    N. Yunes, K. G. Arun, E. Berti, and C. M. Will, Phys. Rev. D 80, 084001 (2009), [Erratum: Phys.Rev.D 89, 109901 (2014)], arXiv:0906.0313 [gr-qc]

    2009 arXiv

  26. [34]

    Nishizawa, A

    A. Nishizawa, A. Taruya, K. Hayama, S. Kawamura, and M.-a. Sakagami, Phys. Rev. D 79, 082002 (2009), arXiv:0903.0528 [astro-ph.CO]

    2009 arXiv

  27. [35]

    S. Khan, S. Husa, M. Hannam, F. Ohme, M. P¨ urrer, X. Jim´ enez Forteza, and A. Boh´ e, Phys. Rev. D 93, 044007 (2016), arXiv:1508.07253 [gr-qc]

    2016 arXiv

  28. [36]

    Yunes and F

    N. Yunes and F. Pretorius, Phys. Rev. D 80, 122003 (2009), arXiv:0909.3328 [gr-qc]

    2009 arXiv

  29. [37]

    Cornish, L

    N. Cornish, L. Sampson, N. Yunes, and F. Pretorius, Phys. Rev. D 84, 062003 (2011), arXiv:1105.2088 [gr-qc]

    2011 arXiv

  30. [38]

    Bayes, Philosophical Transactions of the Royal Society of London , 370 (1973)

    T. Bayes, Philosophical Transactions of the Royal Society of London , 370 (1973)

    1973

  31. [39]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Class. Quant. Grav. 37, 055002 (2020), arXiv:1908.11170 [gr- qc]

    2020 arXiv

  32. [40]

    Capote et al., (2024), arXiv:2411.14607 [gr-qc]

    E. Capote et al., (2024), arXiv:2411.14607 [gr-qc]

    2024 arXiv

  33. [41]

    Acernese et al

    F. Acernese et al. (Virgo), Phys. Rev. Lett. 123, 231108 (2019)

    2019

  34. [42]

    Ashton et al., Astrophys

    G. Ashton et al., Astrophys. J. Suppl. 241, 27 (2019), arXiv:1811.02042 [astro-ph.IM]

    2019 arXiv

  35. [43]

    Higson, W

    E. Higson, W. Handley, M. Hobson, and A. Lasenby, Statistics and Computing 29, 891–913 (2018)

    2018

  36. [44]

    J. S. Speagle, Mon. Not. Roy. Astron. Soc. 493, 3132 (2020), arXiv:1904.02180 [astro-ph.IM]

    2020 arXiv

  37. [45]

    I. M. Romero-Shaw et al., Mon. Not. Roy. Astron. Soc. 499, 3295 (2020), arXiv:2006.00714 [astro-ph.IM]

    2020 arXiv

  38. [46]

    Buonanno, B

    A. Buonanno, B. Iyer, E. Ochsner, Y. Pan, and B. S. Sathyaprakash, Phys. Rev. D 80, 084043 (2009), arXiv:0907.0700 [gr-qc]

    2009 arXiv

  39. [47]

    LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, L VK Algorithm Library - LAL- Suite, Free software (GPL) (2018)

    2018

  40. [48]

    P. A. R. Ade et al. (Planck), Astron. Astrophys. 594, A13 (2016), arXiv:1502.01589 [astro-ph.CO]

    2016 arXiv

  41. [49]

    Vitale, R

    S. Vitale, R. Lynch, J. Veitch, V. Raymond, and R. Sturani, Phys. Rev. Lett. 112, 251101 (2014), arXiv:1403.0129 [gr-qc]

    2014 arXiv

  42. [50]

    Vitale and H.-Y

    S. Vitale and H.-Y. Chen, Phys. Rev. Lett. 121, 021303 (2018), arXiv:1804.07337 [astro-ph.CO]

    2018 arXiv

  43. [51]

    H.-Y. Chen, S. Vitale, and R. Narayan, Phys. Rev. X 9, 031028 (2019), arXiv:1807.05226 [astro-ph.HE]

    2019 arXiv

  44. [52]

    Chassande-Mottin, K

    E. Chassande-Mottin, K. Leyde, S. Mastrogiovanni, and D. A. Steer, Phys. Rev. D 100, 083514 (2019), arXiv:1906.02670 [astro-ph.CO]

    2019 arXiv

  45. [53]

    Punturo et al., Class

    M. Punturo et al., Class. Quant. Grav.27, 194002 (2010)

    2010

  46. [54]

    Reitze et al., Bull

    D. Reitze et al., Bull. Am. Astron. Soc. 51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    2019 arXiv

  47. [55]

    Watarai, A

    D. Watarai, A. Nishizawa, and K. Cannon, Phys. Rev. D 109, 084058 (2024), arXiv:2309.14061 [gr-qc]

    2024

  48. [56]

    London, S

    L. London, S. Khan, E. Fauchon-Jones, C. Garc ´ ıa, M. Hannam, S. Husa, X. Jim´ enez-Forteza, C. Kalaghatgi, F. Ohme, and F. Pannarale, Phys. Rev. Lett.120, 161102 (2018), arXiv:1708.00404 [gr-qc]

    2018 arXiv

  49. [57]

    Abbott et al

    R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 102, 043015 (2020), arXiv:2004.08342 [astro-ph.HE]

    2020 arXiv

  50. [58]

    Tsutsui, A

    T. Tsutsui, A. Nishizawa, and S. Morisaki, Phys. Rev. D 104, 064013 (2021), arXiv:2011.06130 [gr-qc]

    2021 arXiv

  51. [59]

    Tsutsui, A

    T. Tsutsui, A. Nishizawa, and S. Morisaki, Mon. Not. Roy. Astron. Soc. 512, 3878 (2022), arXiv:2107.12531 [gr-qc]

    2022 arXiv

  52. [60]

    Akutsu et al.(KAGRA), PTEP 2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

    T. Akutsu et al.(KAGRA), PTEP 2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

    2021

  53. [61]

    Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, and H. Ya- mamoto (KAGRA), Phys. Rev. D 88, 043007 (2013), arXiv:1306.6747 [gr-qc]

    2013 arXiv

  54. [62]

    Somiya (KAGRA), Class

    K. Somiya (KAGRA), Class. Quant. Grav. 29, 124007 (2012), arXiv:1111.7185 [gr-qc]

    2012 arXiv

  55. [63]

    C. S. Unnikrishnan, Int. J. Mod. Phys. D 22, 1341010 (2013), arXiv:1510.06059 [physics.ins-det]

    2013 arXiv

  56. [64]

    S. M. Gaebel and J. Veitch, Class. Quant. Grav. 34, 174003 (2017), arXiv:1703.08988 [astro-ph.IM]

    2017 arXiv

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Reviewed August 10, 2026 · model on record in the stance chip above.