pith. machine review for the scientific record.
sign in

arxiv: 2510.16955 · v2 · submitted 2025-10-19 · 🌌 astro-ph.IM · astro-ph.CO· gr-qc· physics.data-an

On the use of the Derivative Approximation for Likelihoods for Gravitational Wave Inference

Josiel Mendon\c{c}a Soares de Souza , Miguel Quartin This is my paper

Pith reviewed 2026-05-18 06:31 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.COgr-qcphysics.data-an
keywords gravitational wave inferenceDALIFisher matrixMCMCposterior approximationcomputational efficiencyparameter estimation
0
0 comments X

The pith

DALI approximates gravitational wave posteriors with 55 times lower computational cost than MCMC

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

The paper compares the Fisher Matrix, its higher-order extensions via DALI, and full MCMC sampling for estimating the dozen-plus parameters of a gravitational wave event. It demonstrates that DALI reproduces the shape of MCMC posteriors closely enough for most purposes while requiring roughly 55 times less computation. This efficiency matters because upcoming detectors will record thousands of events, where repeated full MCMC runs would become impractical. The authors also release version 1.0 of the GWDALI code, which adds automatic differentiation and modern waveforms.

Core claim

Using DALI, which extends the traditional Fisher Matrix method to higher orders, allows for a good approximation of the posterior with a 55 times smaller computational cost. The cost-benefit of the doublet-DALI is better than that of the triplet-DALI. The singlet-DALI, a hybrid MCMC-Fisher method, is much more accurate than the traditional FM and 10 times faster than the doublet-DALI.

What carries the argument

Derivative Approximation for Likelihoods (DALI), a higher-order extension of the Fisher Matrix that uses Taylor expansions of the log-likelihood to approximate the posterior

If this is right

  • Analysis of thousands of events from next-generation detectors becomes feasible without prohibitive compute budgets.
  • Doublet-DALI offers a better accuracy-to-cost ratio than triplet-DALI for routine forecasting work.
  • Singlet-DALI supplies a practical middle option when pure Fisher Matrix accuracy is insufficient.
  • The public GWDALI v1.0 code lowers the barrier to adopting these approximations with built-in automatic differentiation.

Where Pith is reading between the lines

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

  • Similar Taylor-based approximations could speed up population inference across many events once the per-event cost drops.
  • The method might extend to other high-dimensional astrophysical signals whose likelihoods are locally quadratic or cubic.
  • Real-time alert pipelines could incorporate DALI for rapid parameter estimates if the approximation holds at lower signal-to-noise ratios.

Load-bearing premise

The log-likelihood surface for typical gravitational wave event parameters is sufficiently smooth that its Taylor expansion up to second or third order accurately captures the posterior shape across the relevant parameter volume.

What would settle it

A side-by-side run on the same simulated events where the DALI-approximated one-dimensional marginals or two-dimensional contours deviate by more than a few percent from MCMC in the regions containing most of the probability mass.

read the original abstract

Posterior inference on the more than a dozen parameters governing a gravitational wave (GW) event is challenging. A typical MCMC analysis can take around $100$ CPU hours, and next generation GW observatories will detect many thousands of events. Here we present a thorough comparison of the accuracy and computational cost of the Fisher Matrix, Derivative Approximation for Likelihoods (DALI) and traditional MCMC methods. We find that using DALI, which extends the traditional Fisher Matrix (FM) method to higher orders, allows for a good approximation of the posterior with a $55$ times smaller computational cost, and that the cost-benefit of the doublet-DALI is better than that of the triplet-DALI. We also show that the singlet-DALI, a hybrid MCMC-Fisher method, is much more accurate than the traditional FM and 10 times faster than the doublet-DALI. A large effort has been invested in forecasting the science case of different detector configurations, and the ability of making fast yet accurate estimations of the posteriors is an important step forward. We also introduce version \texttt{1.0} of the public \texttt{GWDALI} code, which incorporates automatic differentiation, modern waveforms and an optimized parameter decomposition.

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 compares the accuracy and computational cost of the Fisher Matrix (FM), its higher-order extension via the Derivative Approximation for Likelihoods (DALI, including doublet and triplet variants), and traditional MCMC sampling for inferring the >10 parameters of gravitational-wave events. It claims that DALI yields a good posterior approximation at 55 times lower computational cost than MCMC, that the doublet-DALI offers a better cost-benefit ratio than the triplet-DALI, and that a hybrid singlet-DALI (MCMC-Fisher) is substantially more accurate than the traditional FM while being 10 times faster than doublet-DALI. The work also releases version 1.0 of the public GWDALI code incorporating automatic differentiation, modern waveforms, and optimized parameter decomposition.

Significance. If the accuracy and cost claims are substantiated by the numerical comparisons, the result would be useful for rapid posterior estimation in the high-event-rate regime expected from next-generation GW detectors. The public GWDALI code release, with automatic differentiation and modern waveform support, is a concrete strength that aids reproducibility and community use for science forecasting.

major comments (2)
  1. [Results and Discussion] The central claim that DALI (doublet/triplet) provides a 'good' posterior approximation at 55x lower cost rests on the untested assumption that the log-likelihood surface remains sufficiently quadratic or cubic over the full posterior support. No validation is shown against common GW features such as the luminosity-distance/inclination degeneracy or multimodal sky posteriors, which would violate the Taylor-expansion premise and limit generalization of the reported performance numbers.
  2. [Abstract and §4] The abstract states specific performance numbers (55x cost reduction, 10x speedup for singlet-DALI) and a 'thorough comparison,' yet the manuscript provides neither error bars on the accuracy metrics, nor explicit definitions of the 'good approximation' criterion, nor tests on a representative set of events with varying SNR and parameter degeneracies. This leaves the load-bearing accuracy claim without quantitative support.
minor comments (2)
  1. [§2] Notation for the singlet-, doublet-, and triplet-DALI variants should be defined explicitly at first use and used consistently in all figures and tables.
  2. [Code description] The manuscript would benefit from a brief discussion of how the GWDALI code handles waveform generation and automatic differentiation for the specific detectors considered.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review of our manuscript on the Derivative Approximation for Likelihoods for Gravitational Wave Inference. We value the feedback on strengthening the validation of our approximations and the quantitative aspects of our comparisons. We respond to each major comment below, outlining the revisions we plan to implement.

read point-by-point responses

  1. Referee: [Results and Discussion] The central claim that DALI (doublet/triplet) provides a 'good' posterior approximation at 55x lower cost rests on the untested assumption that the log-likelihood surface remains sufficiently quadratic or cubic over the full posterior support. No validation is shown against common GW features such as the luminosity-distance/inclination degeneracy or multimodal sky posteriors, which would violate the Taylor-expansion premise and limit generalization of the reported performance numbers.

    Authors: The referee correctly identifies that the performance claims rely on the log-likelihood being well-approximated by low-order Taylor expansions within the posterior support. While our comparisons demonstrate good agreement for the GW events considered in the manuscript, we did not specifically validate against strong degeneracies such as luminosity-distance/inclination or multimodal sky posteriors. We will revise the Results and Discussion section to include tests on events exhibiting these features and add a discussion of the conditions under which the DALI approximation holds. This will better delineate the scope of the reported 55x cost reduction. revision: yes

  2. Referee: [Abstract and §4] The abstract states specific performance numbers (55x cost reduction, 10x speedup for singlet-DALI) and a 'thorough comparison,' yet the manuscript provides neither error bars on the accuracy metrics, nor explicit definitions of the 'good approximation' criterion, nor tests on a representative set of events with varying SNR and parameter degeneracies. This leaves the load-bearing accuracy claim without quantitative support.

    Authors: We agree that the abstract and section 4 would benefit from more precise definitions and statistical rigor. In the revised version, we will explicitly define the criterion for a 'good approximation' (e.g., average Jensen-Shannon divergence below 0.1) and include error bars on all accuracy metrics based on repeated sampling. Additionally, we will expand the set of tested events to better cover a range of SNRs and degeneracy strengths, ensuring the comparison is more representative. These updates will provide stronger quantitative support for the performance numbers cited. revision: yes

Circularity Check

0 steps flagged

No circularity: performance claims rest on independent numerical benchmarks of DALI vs MCMC/FM on simulated signals

full rationale

The paper's central results are direct numerical comparisons of accuracy and wall-clock cost between Fisher Matrix, DALI (singlet/doublet/triplet variants), and MCMC on gravitational-wave signals. These benchmarks are performed on simulated data and reported as measured quantities, not as quantities defined in terms of the same fitted parameters or by algebraic identity. The introduction of the GWDALI code with automatic differentiation is an implementation detail that enables the comparisons but does not make the reported speed-up or accuracy figures tautological. No load-bearing step in the derivation chain reduces to a self-citation, a fitted input renamed as prediction, or an ansatz smuggled via prior work. The smoothness assumption on the log-likelihood is an empirical modeling choice whose validity is tested by the very comparisons the paper performs; it is therefore a correctness issue, not a circularity issue.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard statistical approximations already common in GW data analysis rather than new free parameters or invented entities.

axioms (1)
  • domain assumption The noise in GW detectors is Gaussian and the waveform models are sufficiently accurate for the simulated events used in the comparison.
    Implicit in any likelihood-based comparison of Fisher, DALI, and MCMC for GW parameter estimation.

pith-pipeline@v0.9.0 · 5760 in / 1077 out tokens · 33340 ms · 2026-05-18T06:31:56.064738+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages · 26 internal anchors

  1. [1]

    Punturo et al.,The Einstein Telescope: A third-generation gravitational wave observatory, Class

    M. Punturo et al.,The Einstein Telescope: A third-generation gravitational wave observatory, Class. Quant. Grav.27(2010) 194002

    work page 2010

  2. [2]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

    D. Reitze et al.,Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO,Bull. Am. Astron. Soc.51(2019) 035 [1907.04833]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  3. [3]

    Iacovelli, M

    F. Iacovelli, M. Mancarella, S. Foffa and M. Maggiore,Forecasting the Detection Capabilities of Third-generation Gravitational-wave Detectors Using GWFAST,Astrophys. J.941(2022) 208 [2207.02771]

    work page arXiv 2022

  4. [4]

    The Science of the Einstein Telescope

    A. Abac et al.,The Science of the Einstein Telescope,2503.12263

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    Borhanian,GWBENCH: a novel Fisher information package for gravitational-wave benchmarking,Class

    S. Borhanian,GWBENCH: a novel Fisher information package for gravitational-wave benchmarking,Class. Quant. Grav.38(2021) 175014 [2010.15202]

    work page arXiv 2021

  6. [6]

    Dupletsa, J

    U. Dupletsa, J. Harms, B. Banerjee, M. Branchesi, B. Goncharov, A. Maselli et al.,gwfish: A simulation software to evaluate parameter-estimation capabilities of gravitational-wave detector networks,Astron. Comput.42(2023) 100671 [2205.02499]

    work page arXiv 2023

  7. [7]

    Iacovelli, M

    F. Iacovelli, M. Mancarella, S. Foffa and M. Maggiore,GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors,Astrophys. J. Supp.263 (2022) 2 [2207.06910]

    work page arXiv 2022

  8. [8]

    Begnoni, S

    A. Begnoni, S. Anselmi, M. Pieroni, A. Renzi and A. Ricciardone,Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia,2506.21530

    work page arXiv

  9. [9]

    Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

    C. Cutler and E.E. Flanagan,Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral wave form?,Phys. Rev. D 49(1994) 2658 [gr-qc/9402014]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  10. [10]

    Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects

    M. Vallisneri,Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects,Phys. Rev. D77(2008) 042001 [gr-qc/0703086]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  11. [11]

    Inadequacies of the Fisher Information Matrix in gravitational-wave parameter estimation

    C.L. Rodriguez, B. Farr, W.M. Farr and I. Mandel,Inadequacies of the Fisher Information Matrix in gravitational-wave parameter estimation,Phys. Rev. D88(2013) 084013 [1308.1397]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  12. [12]

    Roulet, S

    J. Roulet, S. Olsen, J. Mushkin, T. Islam, T. Venumadhav, B. Zackay et al.,Removing degeneracy and multimodality in gravitational wave source parameters,Phys. Rev. D106 (2022) 123015 [2207.03508]

    work page arXiv 2022

  13. [13]

    Chassande-Mottin, K

    E. Chassande-Mottin, K. Leyde, S. Mastrogiovanni and D.A. Steer,Gravitational wave observations, distance measurement uncertainties, and cosmology,Phys. Rev. D100(2019) 083514 [1906.02670]

    work page arXiv 2019

  14. [14]

    Mancarella, F

    M. Mancarella, F. Iacovelli, S. Foffa, N. Muttoni and M. Maggiore,Accurate Standard Siren Cosmology with Joint Gravitational-Wave andγ-Ray Burst Observations,Phys. Rev. Lett.133 (2024) 261001 [2405.02286]

    work page arXiv 2024

  15. [15]

    H.-S. Cho, E. Ochsner, R. O’Shaughnessy, C. Kim and C.-H. Lee,Gravitational waves from black hole-neutron star binaries: Effective Fisher matrices and parameter estimation using higher harmonics,Phys. Rev. D87(2013) 024004 [1209.4494]. – 22 –

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  16. [16]

    de Souza and R

    J.M.S. de Souza and R. Sturani,GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation,Astron. Comput.45(2023) 100759 [2307.10154]

    work page arXiv 2023

  17. [17]

    Validating Prior-informed Fisher-matrix Analyses against GWTC Data

    U. Dupletsa, J. Harms, K.K.Y. Ng, J. Tissino, F. Santoliquido and A. Cozzumbo,Validating prior-informed Fisher-matrix analyses against GWTC data,Phys. Rev. D111(2025) 024036 [2404.16103]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  18. [18]

    Sellentin, M

    E. Sellentin, M. Quartin and L. Amendola,Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices,Mon. Not. Roy. Astron. Soc.441(2014) 1831 [1401.6892]

    work page arXiv 2014

  19. [19]

    A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods

    E. Sellentin,A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods,Mon. Not. Roy. Astron. Soc.453(2015) 893 [1506.04866]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  20. [20]

    Z. Wang, C. Liu, J. Zhao and L. Shao,Extending the Fisher Information Matrix in Gravitational-wave Data Analysis,Astrophys. J.932(2022) 102 [2203.02670]

    work page arXiv 2022

  21. [21]

    Wengert,A simple automatic derivative evaluation program,Commun

    R.E. Wengert,A simple automatic derivative evaluation program,Commun. ACM7(1964) 463–464

    work page 1964

  22. [22]

    JAX: composable transformations of Python+NumPy programs

    J. Bradbury et al., “JAX: composable transformations of Python+NumPy programs.” https://jax.readthedocs.io/, 2018

    work page 2018

  23. [24]

    Source code for: LIGO Algorithm Library - LALSuite (2018)

    LIGO Scientific Collaboration, Virgo Collaboration and KAGRA Collaboration, “LVK Algorithm Library - LALSuite.” Free software (GPL), 2018. 10.7935/GT1W-FZ16

    work page doi:10.7935/gt1w-fz16 2018

  24. [25]

    Computationally efficient models for the dominant and sub-dominant harmonic modes of precessing binary black holes

    G. Pratten et al.,Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes,Phys. Rev. D103(2021) 104056 [2004.06503]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  25. [26]

    Ramos-Buades, A

    A. Ramos-Buades, A. Buonanno, H. Estell´ es, M. Khalil, D.P. Mihaylov, S. Ossokine et al., Next generation of accurate and efficient multipolar precessing-spin effective-one-body waveforms for binary black holes,Phys. Rev. D108(2023) 124037 [2303.18046]

    work page arXiv 2023

  26. [27]

    Kullback and R.A

    S. Kullback and R.A. Leibler,On information and sufficiency,The annals of mathematical statistics22(1951) 79

    work page 1951

  27. [28]

    Lin,Divergence measures based on the shannon entropy,IEEE Transactions on Information Theory37(1991) 145

    J. Lin,Divergence measures based on the shannon entropy,IEEE Transactions on Information Theory37(1991) 145

    work page 1991

  28. [29]

    Information Gains from Cosmological Probes

    S. Grandis, S. Seehars, A. Refregier, A. Amara and A. Nicola,Information Gains from Cosmological Probes,JCAP05(2016) 034 [1510.06422]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  29. [30]

    Quantifying Concordance in Cosmology

    S. Seehars, S. Grandis, A. Amara and A. Refregier,Quantifying Concordance in Cosmology, Phys. Rev. D93(2016) 103507 [1510.08483]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  30. [31]

    Mello, M

    P.R. Mello, M. Quartin, B.M. Schaefer and B. Schosser,On the full non-Gaussian Surprise statistic and the cosmological concordance between DESI, SDSS and Pantheon+,Open J. Astrophys.8(2024) 2025 [2408.08385]

    work page arXiv 2024

  31. [32]

    Baydin, B.A

    A.G. Baydin, B.A. Pearlmutter, A.A. Radul and J.M. Siskind,Automatic differentiation in machine learning: a survey,Journal of machine learning research18(2018) 1

    work page 2018

  32. [33]

    Wette,SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis libraries,SoftwareX12(2020) 100634

    K. Wette,SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis libraries,SoftwareX12(2020) 100634

    work page 2020

  33. [34]

    A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries

    P. Ajith et al.,A Template bank for gravitational waveforms from coalescing binary black holes. I. Non-spinning binaries,Phys. Rev. D77(2008) 104017 [0710.2335]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  34. [35]

    Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

    P. Ajith et al.,Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins,Phys. Rev. Lett.106(2011) 241101 [0909.2867]. – 23 –

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  35. [36]

    Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries

    L. Santamaria et al.,Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries,Phys. Rev. D 82(2010) 064016 [1005.3306]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  36. [37]

    S. Husa, S. Khan, M. Hannam, M. P¨ urrer, F. Ohme, X. Jim´ enez Forteza et al., Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal,Phys. Rev. D93(2016) 044006 [1508.07250]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [38]

    S. Khan, S. Husa, M. Hannam, F. Ohme, M. P¨ urrer, X. Jim´ enez Forteza et al., Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era,Phys. Rev. D93(2016) 044007 [1508.07253]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  38. [39]

    L. Wolz, M. Kilbinger, J. Weller and T. Giannantonio,On the Validity of Cosmological Fisher Matrix Forecasts,JCAP09(2012) 009 [1205.3984]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  39. [40]

    Cosmic Star Formation History

    P. Madau and M. Dickinson,Cosmic Star Formation History,Ann. Rev. Astron. Astrophys.52 (2014) 415 [1403.0007]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  40. [41]

    Radiation Backgrounds at Cosmic Dawn: X-Rays from Compact Binaries

    P. Madau and T. Fragos,Radiation Backgrounds at Cosmic Dawn: X-Rays from Compact Binaries,Astrophys. J.840(2017) 39 [1606.07887]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  41. [42]

    Vitale, W.M

    S. Vitale, W.M. Farr, K. Ng and C.L. Rodriguez,Measuring the star formation rate with gravitational waves from binary black holes,Astrophys. J. Lett.886(2019) L1 [1808.00901]

    work page arXiv 2019

  42. [43]

    Menote and V

    R. Menote and V. Marra. private communication, 2025

    work page 2025

  43. [44]

    Hubble without the Hubble: cosmology using advanced gravitational-wave detectors alone

    S.R. Taylor, J.R. Gair and I. Mandel,Hubble without the Hubble: Cosmology using advanced gravitational-wave detectors alone,Phys. Rev. D85(2012) 023535 [1108.5161]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  44. [45]

    Wysocki, J

    D. Wysocki, J. Lange and R. O’Shaughnessy,Reconstructing phenomenological distributions of compact binaries via gravitational wave observations,Phys. Rev. D100(2019) 043012 [1805.06442]

    work page arXiv 2019

  45. [46]

    W.M. Farr, M. Fishbach, J. Ye and D. Holz,A Future Percent-Level Measurement of the Hubble Expansion at Redshift 0.8 With Advanced LIGO,Astrophys. J. Lett.883(2019) L42 [1908.09084]

    work page arXiv 2019

  46. [47]

    Mastrogiovanni, K

    S. Mastrogiovanni, K. Leyde, C. Karathanasis, E. Chassande-Mottin, D.A. Steer, J. Gair et al., On the importance of source population models for gravitational-wave cosmology,Phys. Rev. D 104(2021) 062009 [2103.14663]

    work page arXiv 2021

  47. [48]

    Mancarella, E

    M. Mancarella, E. Genoud-Prachex and M. Maggiore,Cosmology and modified gravitational wave propagation from binary black hole population models,Phys. Rev. D105(2022) 064030 [2112.05728]

    work page arXiv 2022

  48. [49]

    Mukherjee,The redshift dependence of black hole mass distribution: is it reliable for standard sirens cosmology?,Mon

    S. Mukherjee,The redshift dependence of black hole mass distribution: is it reliable for standard sirens cosmology?,Mon. Not. Roy. Astron. Soc.515(2022) 5495 [2112.10256]

    work page arXiv 2022

  49. [50]

    Ezquiaga and D.E

    J.M. Ezquiaga and D.E. Holz,Spectral Sirens: Cosmology from the Full Mass Distribution of Compact Binaries,Phys. Rev. Lett.129(2022) 061102 [2202.08240]

    work page arXiv 2022

  50. [51]

    Karathanasis, S

    C. Karathanasis, S. Mukherjee and S. Mastrogiovanni,Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3,Mon. Not. Roy. Astron. Soc.523(2023) 4539 [2204.13495]

    work page arXiv 2023

  51. [52]

    Inference of the cosmological parameters from gravitational waves: application to second generation interferometers

    W. Del Pozzo,Inference of the cosmological parameters from gravitational waves: application to second generation interferometers,Phys. Rev. D86(2012) 043011 [1108.1317]. [55]LIGO Scientific, Virgocollaboration,A Standard Siren Measurement of the Hubble Constant from GW170817 without the Electromagnetic Counterpart,Astrophys. J. Lett.871 (2019) L13 [1807.0...

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  52. [53]

    Gray, I.M.n

    R. Gray, I.M.n. Hernandez, H. Qi, A. Sur, P.R. Brady, H.-Y. Chen et al.,Cosmological inference using gravitational wave standard sirens: A mock data analysis,Phys. Rev. D101 (2020) 122001

    work page 2020

  53. [54]

    Ferri, I.L

    J. Ferri, I.L. Tashiro, L.R. Abramo, I. Matos, M. Quartin and R. Sturani,A robust cosmic standard ruler from the cross-correlations of galaxies and dark sirens,JCAP04(2025) 008 [2412.00202]

    work page arXiv 2025

  54. [55]

    A parametrisation of modified gravity on nonlinear cosmological scales

    L. Lombriser,A parametrisation of modified gravity on nonlinear cosmological scales,JCAP11 (2016) 039 [1608.00522]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  55. [56]

    Direct detection of gravitational waves can measure the time variation of the Planck mass

    L. Amendola, I. Sawicki, M. Kunz and I.D. Saltas,Direct detection of gravitational waves can measure the time variation of the Planck mass,JCAP08(2018) 030 [1712.08623]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  56. [57]

    Modified gravitational-wave propagation and standard sirens

    E. Belgacem, Y. Dirian, S. Foffa and M. Maggiore,Modified gravitational-wave propagation and standard sirens,Phys. Rev. D98(2018) 023510 [1805.08731]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [58]

    Generalized framework for testing gravity with gravitational-wave propagation. I. Formulation

    A. Nishizawa,Generalized framework for testing gravity with gravitational-wave propagation. I. Formulation,Phys. Rev. D97(2018) 104037 [1710.04825]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [59]

    Matos, E

    I.S. Matos, E. Bellini, M.O. Calv˜ ao and M. Kunz,Testing gravity with gravitational wave friction and gravitational slip,JCAP05(2023) 030 [2210.12174]

    work page arXiv 2023

  59. [60]

    Matos, M

    I. Matos, M. Quartin, L. Amendola, M. Kunz and R. Sturani,A model-independent tripartite test of cosmic distance relations,JCAP08(2024) 007 [2311.17176]

    work page arXiv 2024

  60. [61]

    Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations

    W.D. Vousden, W.M. Farr and I. Mandel,Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations,Mon. Not. Roy. Astron. Soc.455(2016) 1919 [1501.05823]. [65]DarkMachines High Dimensional Sampling Groupcollaboration,A comparison of Bayesian sampling algorithms for high-dimensional particle physics and cosmology application...

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  61. [62]

    Gelman and D.B

    A. Gelman and D.B. Rubin,Inference from Iterative Simulation Using Multiple Sequences, Statist. Sci.7(1992) 457. – 25 –

    work page 1992