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Accelerated Sequential Posterior Inference via Reuse for Gravitational-Wave Analyses

Michael J. Williams*

  • *Contact author: michael.williams3@port.ac.uk

Phys. Rev. Lett. 137, 021410 – Published 10 July, 2026

DOI: https://doi.org/10.1103/5hvn-3lmh

Abstract

We introduce accelerated sequential posterior inference via reuse (ASPIRE), a broadly applicable framework that transforms existing posterior samples and Bayesian evidence estimates into unbiased results under alternative models without rerunning the original analysis. ASPIRE combines normalizing flows with a generalized sequential Monte Carlo (SMC) scheme, enabling efficient updates of existing results and reducing total likelihood evaluations and wall times by factors of up to 5.8 and 5.5, respectively, with larger gains per posterior sample. This addresses a growing problem in gravitational-wave astronomy, where events must be repeatedly reanalyzed under different models or physical hypotheses. We show that ASPIRE reproduces full Bayesian results when switching waveform models or adding physical effects such as spin precession and orbital eccentricity. With this statistical robustness, ASPIRE turns repeated reanalyses into fast, reliable updates—paving the way for systematic studies of waveform systematics, scalable reanalyses across large event catalogs, and broadly applicable Bayesian reanalysis across other scientific domains.

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References (128)

  1. J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  2. F. Acernese et al. (VIRGO Collaboration), Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  3. T. Akutsu et al. (KAGRA Collaboration), Overview of KAGRA: Detector design and construction history, Prog. Theor. Exp. Phys. 2021, 05A101 (2021).
  4. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, Phys. Rev. X 9, 031040 (2019).
  5. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), GWTC-2: Compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. X 11, 021053 (2021).
  6. R. Abbott et al. (LIGO Scientific and VIRGO Collaborations), GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. D 109, 022001 (2024).
  7. R. Abbott et al. (KAGRA, VIRGO, and LIGO Scientific Collaborations), GWTC-3: Compact clby LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  8. GWTC-4.0: Updating the gravitational-wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, arXiv:2508.18082.
  9. LIGO Scientific Collaboration, LIGO-G2302098: LIGO-Virgo-KAGRA cumulative detection plot—O1-O4b, https://dcc.ligo.org/LIGO-G2302098-v15/public (2025), accessed: July 7, 2025.
  10. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Constraints on the cosmic expansion history from GWTC–3, Astrophys. J. 949, 76 (2023).
  11. GWTC-4.0: Constraints on the cosmic expansion rate and modified gravitational-wave propagation, arXiv:2509.04348.
  12. R. Gamba, M. Breschi, S. Bernuzzi, M. Agathos, and A. Nagar, Waveform systematics in the gravitational-wave inference of tidal parameters and equation of state from binary neutron star signals, Phys. Rev. D 103, 124015 (2021).
  13. A. B. Yelikar, R. O. Shaughnessy, J. Lange, and A. Z. Jan, Waveform systematics in gravitational-wave inference of signals from binary neutron star merger models incorporating higher-order modes information, Phys. Rev. D 110, 064024 (2024).
  14. A. Gamboa et al., Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM, Phys. Rev. D 112, 044038 (2025).
  15. A. Nagar, R. Gamba, P. Rettegno, V. Fantini, and S. Bernuzzi, Effective-one-body waveform model for noncircularized, planar, coalescing black hole binaries: The importance of radiation reaction, Phys. Rev. D 110, 084001 (2024).
  16. N. V. Krishnendu and F. Ohme, Testing general relativity with gravitational waves: An overview, Universe 7, 497 (2021).
  17. R. Abbott et al. (LIGO Scientific and VIRGO Collaborations), Search for lensing signatures in the gravitational-wave observations from the first half of LIGO–Virgo’s third observing run, Astrophys. J. 923, 14 (2021).
  18. J. Skilling, Nested sampling, AIP Conf. Proc. 735, 395 (2004).
  19. J. Skilling, Nested sampling for general Bayesian computation, Bayesian Anal. 1, 833 (2006).
  20. J. Veitch et al., Parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library, Phys. Rev. D 91, 042003 (2015).
  21. I. M. Romero-Shaw et al., Bayesian inference for compact binary coalescences with bilby: Validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. R. Astron. Soc. 499, 3295 (2020).
  22. M. J. Williams, J. Veitch, and C. Messenger, Nested sampling with normalizing flows for gravitational-wave inference, Phys. Rev. D 103, 103006 (2021).
  23. M. J. Williams, J. Veitch, and C. Messenger, Importance nested sampling with normalising flows, Mach. Learn. Sci. Tech. 4, 035011 (2023).
  24. A. J. K. Chua and M. Vallisneri, Learning Bayesian posteriors with neural networks for gravitational-wave inference, Phys. Rev. Lett. 124, 041102 (2020).
  25. H. Gabbard, C. Messenger, I. S. Heng, F. Tonolini, and R. Murray-Smith, Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy, Nat. Phys. 18, 112 (2022).
  26. M. Dax, S. R. Green, J. Gair, M. Pürrer, J. Wildberger, J. H. Macke, A. Buonanno, and B. Schölkopf, Neural importance sampling for rapid and reliable gravitational-wave inference, Phys. Rev. Lett. 130, 171403 (2023).
  27. S. Fairhurst, C. Hoy, R. Green, C. Mills, and S. A. Usman, Simple parameter estimation using observable features of gravitational-wave signals, Phys. Rev. D 108, 082006 (2023).
  28. G. Ashton, Reconstructing and resampling: A guide to utilising posterior samples from gravitational wave observations, RAS Tech. Instrum. 5, rzag012 (2026).
  29. J. Lange, R. O’Shaughnessy, and M. Rizzo, Rapid and accurate parameter inference for coalescing, precessing compact binaries, arXiv:1805.10457.
  30. M. Prathaban, H. Bevins, and W. Handley, Accelerated nested sampling with β-flows for gravitational waves, Mon. Not. R. Astron. Soc. 541, 200 (2025).
  31. M. Prathaban, C. Hoy, and M. J. Williams, Leveraging rapid parameter estimates for efficient gravitational-wave Bayesian inference via posterior repartitioning, arXiv:2601.21630.
  32. D. W. Hogg and D. Foreman-Mackey, Data analysis recipes: Using Markov Chain Monte Carlo, Astrophys. J. Suppl. Ser. 236, 11 (2018).
  33. D. J. Earl and M. W. Deem, Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys. (Incorporating Faraday Transactions) 7, 3910 (2005).
  34. G. Ashton and C. Talbot, bilby-mcmc: An MCMC sampler for gravitational-wave inference, Mon. Not. R. Astron. Soc. 507, 2037 (2021).
  35. N. E. Wolfe, C. Talbot, and J. Golomb, Accelerating tests of general relativity with gravitational-wave signals using hybrid sampling, Phys. Rev. D 107, 104056 (2023).
  36. M. Falxa, S. Babak, and M. Le Jeune, Adaptive kernel density estimation proposal in gravitational wave data analysis, Phys. Rev. D 107, 022008 (2023).
  37. T. B. Littenberg and N. J. Cornish, Prototype global analysis of LISA data with multiple source types, Phys. Rev. D 107, 063004 (2023).
  38. N. Korsakova, S. Babak, M. L. Katz, N. Karnesis, S. Khukhlaev, and J. R. Gair, Neural density estimation for Galactic binaries in the LISA data analysis, Phys. Rev. D 110, 104069 (2024).
  39. P. C. Peters and J. Mathews, Gravitational radiation from point masses in a Keplerian orbit, Phys. Rev. 131, 435 (1963).
  40. T. A. Apostolatos, C. Cutler, G. J. Sussman, and K. S. Thorne, Spin induced orbital precession and its modulation of the gravitational wave forms from merging binaries, Phys. Rev. D 49, 6274 (1994).
  41. G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mohamed, and B. Lakshminarayanan, Normalizing flows for probabilistic modeling and inference, J. Mach. Learn. Res. 22, 2617 (2021), http://jmlr.org/papers/v22/19-1028.html.
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/5hvn-3lmh for additional implementation and analysis details, which includes Refs. [43–59].
  43. M. Karamanis, D. Nabergoj, F. Beutler, J. A. Peacock, and U. Seljak, pocomc: A python package for accelerated Bayesian inference in astronomy and cosmology, J. Open Source Software 7, 4634 (2022).
  44. A. W. v. d. Vaart, Delta method, in Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, Cambridge, England, 1998), pp. 25–34.
  45. R. Douc and O. Cappé, Comparison of resampling schemes for particle filtering, in ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005 (IEEE, New York, 2005), pp. 64–69.
  46. R. D. P. Grumitt, M. Karamanis, and U. Seljak, Sequential Kalman tuning of the t-preconditioned Crank-Nicolson algorithm: Efficient adaptive and gradient-free inference for Bayesian inverse problems, Inverse Probl. 40, 125023 (2024).
  47. N. Bose and A. Pai, Effective chirp mass in the inspiral frequency evolution of the nonspinning eccentric compact binary, Phys. Rev. D 104, 124021 (2021).
  48. G. Papamakarios, T. Pavlakou, and I. Murray, Masked autoregressive flow for density estimation, arXiv:1705.07057.
  49. D. Ward, Flowjax: Distributions and normalizing flows in jax, 10.5281/zenodo.10402073 (2025).
  50. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  51. I. Loshchilov and F. Hutter, SGDR: Stochastic gradient descent with warm restarts, arXiv:1608.03983.
  52. B. P. Abbott et al. (KAGRA, LIGO Scientific, and Virgo Collaborations), Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Relativity 19, 1 (2016).
  53. E. Baird, S. Fairhurst, M. Hannam, and P. Murphy, Degeneracy between mass and spin in black-hole-binary waveforms, Phys. Rev. D 87, 024035 (2013).
  54. E. Thrane and C. Talbot, An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models, Pub. Astron. Soc. Aust. 36, e010 (2019); 37, e036(E) (2020).
  55. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
  56. E. Hellinger, Neue begründung der theorie quadratischer formen von unendlichvielen veränderlichen, J. Reine Angew. Math. 136, 210 (1909).
  57. J. Annis, N. J. Evans, B. J. Miller, and T. J. Palmeri, Thermodynamic integration and steppingstone sampling methods for estimating bayes factors: A tutorial, J. Math. Psychol. 89, 67 (2019).
  58. A. Gelman and D. B. Rubin, Inference from iterative simulation using multiple sequences, Stat. Sci. 7, 457 (1992).
  59. M. J. Williams, J. Veitch, and C. Chapman-Bird, mj-will/nessai: v0.15.2, 10.5281/zenodo.18711786 (2026).
  60. M. J. Williams, M. Karamanis, Y. Luo, and U. Seljak, Validating sequential Monte Carlo for gravitational-wave inference, Mon. Not. R. Astron. Soc. 543, 1479 (2025).
  61. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, M. West, J. M. Bernardo, M. J. Bayarri et al., Sequential Monte Carlo for Bayesian Computation (Oxford University Press, Oxford, UK, 2007), 10.1093/oso/9780199214655.003.0005.
  62. P. Del Moral, A. Doucet, and A. Jasra, An adaptive sequential Monte Carlo method for approximate Bayesian computation, Stat. Comput. 22, 1009 (2012).
  63. P. Fearnhead and B. M. Taylor, An adaptive sequential Monte Carlo sampler, Bayesian Anal. 8, 411 (2013).
  64. M. J. Williams, A. Garron, F. Santoliquido, J. Tissino, and K. Leyde, mj-will/aspire: v0.1.0a19, 10.5281/zenodo.19224148 (2026).
  65. G. Pratten et al., Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D 103, 104056 (2021).
  66. J. E. Thompson, E. Hamilton, L. London, S. Ghosh, P. Kolitsidou, C. Hoy, and M. Hannam, PhenomXO4a: A phenomenological gravitational-wave model for precessing black-hole binaries with higher multipoles and asymmetries, Phys. Rev. D 109, 063012 (2024).
  67. S. Husa, S. Khan, M. Hannam, M. Pürrer, F. Ohme, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal, Phys. Rev. D 93, 044006 (2016).
  68. S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era, Phys. Rev. D 93, 044007 (2016).
  69. P. Schmidt, M. Hannam, and S. Husa, Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals, Phys. Rev. D 86, 104063 (2012).
  70. M. Hannam, P. Schmidt, A. Bohé, L. Haegel, S. Husa, F. Ohme, G. Pratten, and M. Pürrer, Simple model of complete precessing black-hole-binary gravitational waveforms, Phys. Rev. Lett. 113, 151101 (2014).
  71. S. Morisaki, R. Smith, L. Tsukada, S. Sachdev, S. Stevenson, C. Talbot, and A. Zimmerman, Rapid localization and inference on compact binary coalescences with the Advanced LIGO-Virgo-KAGRA gravitational-wave detector network, Phys. Rev. D 108, 123040 (2023).
  72. I. Mandel and F. S. Broekgaarden, Rates of compact object coalescences, Living Rev. Relativity 25, 1 (2022).
  73. I. M. Romero-Shaw, P. D. Lasky, E. Thrane, and J. C. Bustillo, GW190521: Orbital eccentricity and signatures of dynamical formation in a binary black hole merger signal, Astrophys. J. Lett. 903, L5 (2020).
  74. I. M. Romero-Shaw, P. D. Lasky, and E. Thrane, Four eccentric mergers increase the evidence that LIGO–Virgo–KAGRA’s binary black holes form dynamically, Astrophys. J. 940, 171 (2022).
  75. N. Gupte et al., Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA, Phys. Rev. D 112, 104045 (2025).
  76. G. Morras, G. Pratten, and P. Schmidt, Orbital eccentricity in a neutron star—black hole binary, Astrophys. J. Lett. 1000, L2 (2026).
  77. A. Buonanno, B. Iyer, E. Ochsner, Y. Pan, and B. S. Sathyaprakash, Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors, Phys. Rev. D 80, 084043 (2009).
  78. B. Moore, M. Favata, K. G. Arun, and C. K. Mishra, Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order, Phys. Rev. D 93, 124061 (2016).
  79. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW150914: First results from the search for binary black hole coalescence with Advanced LIGO, Phys. Rev. D 93, 122003 (2016).
  80. A. H. Nitz, S. Kumar, Y.-F. Wang, S. Kastha, S. Wu, M. Schäfer, R. Dhurkunde, and C. D. Capano, 4-OGC: Catalog of gravitational waves from compact binary mergers, Astrophys. J. 946, 59 (2023).
  81. M. Hannam et al., General-relativistic precession in a black-hole binary, Nature (London) 610, 652 (2022).
  82. E. Payne, S. Hourihane, J. Golomb, R. Udall, R. Udall, D. Davis, and K. Chatziioannou, Curious case of GW200129: Interplay between spin-precession inference and data-quality issues, Phys. Rev. D 106, 104017 (2022).
  83. R. Macas, A. Lundgren, and G. Ashton, Revisiting the evidence for precession in GW200129 with machine learning noise mitigation, Phys. Rev. D 109, 062006 (2024).
  84. A. Viets et al., Reconstructing the calibrated strain signal in the Advanced LIGO detectors, Classical Quantum Gravity 35, 095015 (2018).
  85. A. G. Abac et al. (LIGO Scientific, VIRGO, and KAGRA Collaborations), GWTC-4.0: Methods for identifying and characterizing gravitational-wave transients, arXiv:2508.18081.
  86. G. Pratten, S. Husa, C. Garcia-Quiros, M. Colleoni, A. Ramos-Buades, H. Estelles, and R. Jaume, Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes, Phys. Rev. D 102, 064001 (2020).
  87. L. Pompili et al., Laying the foundation of the effective-one-body waveform models SEOBNRv5: Improved accuracy and efficiency for spinning nonprecessing binary black holes, Phys. Rev. D 108, 124035 (2023).
  88. W. D. Vousden, W. M. Farr, and I. Mandel, Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations, Mon. Not. R. Astron. Soc. 455, 1919 (2016).
  89. M. M. Graham and A. J. Storkey, Continuously tempered Hamiltonian Monte Carlo, arXiv:1704.03338.
  90. A. Buchholz, N. Chopin, and P. E. Jacob, Adaptive tuning of Hamiltonian Monte Carlo within sequential Monte Carlo, Bayesian Anal. 16, 745 (2021).
  91. T. Le Thu Nguyen, F. Septier, G. W. Peters, and Y. Delignon, Improving SMC sampler estimate by recycling all past simulated particles, in 2014 IEEE Workshop on Statistical Signal Processing (SSP) (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2014), pp. 117–120, 10.1109/SSP.2014.6884589.
  92. M. Karamanis and U. Seljak, Persistent sampling: Enhancing the efficiency of sequential Monte Carlo, Stat. Comput. 35, 1 (2025).
  93. R. M. Neal, Annealed importance sampling, arXiv:physics/9803008.
  94. S. Syed, A. Bouchard-Côté, K. Chern, and A. Doucet, Optimised annealed sequential Monte Carlo samplers, arXiv:2408.12057.
  95. A. H. Nitz, Robust, rapid, and simple gravitational-wave parameter estimation, Phys. Rev. D 112, 023032 (2025).
  96. G. Cabourn Davies et al., Premerger observation and characterization of massive black hole binaries, Phys. Rev. D 111, 043045 (2025).
  97. L. Gärtner, N. Hartmann, L. Heinrich, M. Horstmann, T. Kuhr, M. Reboud, S. Stefkova, and D. van Dyk, Constructing model-agnostic likelihoods, a method for the reinterpretation of particle physics results, Eur. Phys. J. C 84, 693 (2024).
  98. R. Arjona, L. Espinosa-Portales, J. García-Bellido, and S. Nesseris, A GREAT model comparison against the cosmological constant, Phys. Dark Universe 36, 101029 (2022).
  99. Z. G. Lane, A. Seifert, R. Ridden-Harper, and D. L. Wiltshire, Cosmological foundations revisited with Pantheon+, Mon. Not. R. Astron. Soc. 536, 1752 (2025).
  100. M. J. Williams, mj-will/aspire-bilby: v0.1.0a2, 10.5281/zenodo.17540602 (2025).
  101. M. J. Williams, mj-will/aspire-gw: v0.1.0a1, 10.5281/zenodo.17183944 (2025).
  102. M. J. Williams, aspire-inference, python Package Index (pypi) (2025), https://pypi.org/project/aspire-inference/.
  103. M. J. Williams, aspire-bilby, python Package Index (pypi) (2025), https://pypi.org/project/aspire-bilby/.
  104. M. J. Williams, aspire-gw, python Package Index (pypi) (2025), https://pypi.org/project/aspire-gw/.
  105. https://github.com/mj-will/aspire.
  106. https://github.com/mj-will/aspire-bilby.
  107. https://github.com/mj-will/aspire-gw.
  108. Consortium for python Data API Standards, array-api-compat, https://pypi.org/project/array-api-compat/ (2025).
  109. G. Ashton et al., bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. Ser. 241, 27 (2019).
  110. C. Talbot et al., bilby-dev/bilby: v2.5.2, 10.5281/zenodo.15586392 (2025).
  111. D. Foreman-Mackey, corner.py: Scatterplot matrices in python, J. Open Source Software 1, 24 (2016).
  112. J. S. Speagle, dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. R. Astron. Soc. 493, 3132 (2020).
  113. M. J. Williams, mj-will/gwflow: v0.1.0a1, 10.5281/zenodo.17182521 (2025).
  114. LIGO Scientific Collaboration, LIGO Algorithm Library—lalsuite, free software (GPL), 10.7935/GT1W-FZ16 (2018).
  115. K. Wette, swiglal: python and Octave interfaces to the lalsuite gravitational-wave data analysis libraries, SoftwareX 12, 100634 (2020).
  116. J. D. Hunter, matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  117. M. J. Williams, mj-will/minipcn, 10.5281/zenodo.15657998 (2025).
  118. C. R. Harris et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  119. C. Hoy and V. Raymond, pesummary: The code agnostic parameter estimation summary page builder, SoftwareX 15, 100765 (2021).
  120. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC Hammer, Publ. Astron. Soc. Pac. 125, 306 (2013).
  121. A. Paszke et al., pytorch: An imperative style, high-performance deep learning library, arXiv:1912.01703.
  122. Wes McKinney, Data structures for statistical computing in python, in Proceedings of the 9th python in Science Conference, edited by Stéfan van der Walt and Jarrod Millman (SciPy Conference, Austin, Texas, USA, 2010), pp. 56—61, 10.25080/Majora-92bf1922-00a.
  123. P. Virtanen et al. (scipy 1.0 Contributors), scipy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  124. M. L. Waskom, seaborn: Statistical data visualization, J. Open Source Software 6, 3021 (2021).
  125. F. Rozet et al., zuko: Normalizing flows in pytorch, 10.5281/zenodo.7625672 (2024).
  126. R. Abbott et al. (LIGO Scientific and Virgo Collaborations), Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo, SoftwareX 13, 100658 (2021).
  127. M. J. Williams, Accelerated Sequential Posterior Inference via Reuse for Gravitational-Wave Analyses—Data Release, 10.5281/zenodo.17514969 (2025).
  128. M. J. Williams, Accelerated Sequential Posterior Inference via Reuse for Gravitational-Wave Analyses—Code Release, 10.5281/zenodo.17536499 (2025).

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