pith. machine review for the scientific record. sign in

arxiv: 2604.24330 · v1 · submitted 2026-04-27 · 🌀 gr-qc · astro-ph.HE· astro-ph.IM

Recognition: unknown

Pre-localization of Massive Black Hole Binaries in the Millihertz Band

Xue-Ting Zhang , Jonathan Gair , Chris Messenger , Natalia Korsakova , Yi-Ming Hu , Hong-Yu Chen
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:16 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEastro-ph.IM
keywords gravitational wavesmassive black hole binariesneural spline flowsearly warningsky localizationBayesian inferenceTianQin
0
0 comments X

The pith

A neural spline flow pipeline delivers pre-merger sky localizations of about 20 square degrees for massive black hole binaries observed by space-borne detectors.

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

The paper develops a fast Bayesian inference method for gravitational wave signals from massive black hole binaries detected by space-based instruments. It pairs a learned embedding of the detector time series with a neural spline flow to generate posterior samples for source parameters in roughly one minute. For a typical system that merges 15 minutes after the observation window ends, the method produces sky localization areas of order 20 square degrees while recovering the same number of sky modes and comparable parameter uncertainties as a slower reference Markov chain Monte Carlo analysis. The speed keeps the entire process inside a useful pre-merger warning interval suitable for triggering electromagnetic observations. These outcomes indicate that flow-based amortized inference can support near-real-time analysis of continuous data streams from future space-borne gravitational wave detectors.

Core claim

For a representative MBHB whose merger occurs ∼15 minutes after the end of the analyzed GW observation, the pipeline achieves pre-merger sky localizations of order ∼20 deg², recovers the same number of sky modes as a reference parallel-tempered Markov chain Monte Carlo (PTMCMC) analysis, and yields parameter uncertainties of comparable scale, while still operating within a practically useful pre-merger warning window.

What carries the argument

Learned embedding of the detector time series combined with a neural spline flow for amortized Bayesian inference that produces posterior samples without repeated likelihood evaluations.

If this is right

  • The pipeline enables low-latency alerts for electromagnetic follow-up observations of MBHB events.
  • Pre-merger localizations around 20 square degrees are tight enough to direct targeted telescopes.
  • The one-minute runtime supports high-throughput processing of ongoing data streams from space-borne detectors.
  • The approach matches traditional sampler accuracy while remaining inside practical early-warning time windows.

Where Pith is reading between the lines

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

  • The same embedding-plus-flow structure could be retrained for other planned space-based detectors to achieve earlier warnings.
  • Extending the training set to include signals with spin precession or higher-order waveform modes would test how far the current accuracy holds.
  • Direct integration of the pipeline into actual detector data-reduction software could further cut end-to-end latency.

Load-bearing premise

The neural network trained only on simulated signals must produce an accurate approximation to the true posterior distribution of the binary parameters without introducing systematic biases.

What would settle it

Compare the neural flow sky localization areas and parameter uncertainties against full parallel-tempered MCMC results on an independent set of simulated MBHB signals whose true parameter values are known in advance.

Figures

Figures reproduced from arXiv: 2604.24330 by Chris Messenger, Hong-Yu Chen, Jonathan Gair, Natalia Korsakova, Xue-Ting Zhang, Yi-Ming Hu.

Figure 1
Figure 1. Figure 1: FIG. 1. P–P plot assessing the calibration of the NSF poste view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of posterior distributions for a representative MBHB injection: PTMCMC (slate blue) computed on view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. NSF sky map for the representative MBHB event in ecliptic coordinates. The yellow triangles mark theoretical view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Histogram of the recovered 90% sky-localization areas view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Posterior comparison for case II, in which the chirp mass is modified relative to the reference injection. The posteriors view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Posterior comparison for case III, in which the symmetric mass ratio is modified relative to the reference injection. view at source ↗
read the original abstract

The space-borne gravitational-wave (GW) detectors will open a new mass and redshift regime, allowing us to observe massive black hole binaries (MBHBs) throughout the Universe. A subset of these systems is expected to produce electromagnetic (EM) counterparts, offering a unique opportunity to follow the continuous evolution of massive black holes through joint GW and EM observations. Realizing this potential, however, requires low-latency, high-throughput data-analysis pipelines that can extract reliable source parameters and sky localizations from space-borne data streams fast enough to trigger EM follow-up. In this work we develop a fast, normalising flow-based inference pipeline designed for early-warning analysis of MBHB signals in a TianQin-like configuration. Our method combines a learned embedding of the detector time series with a neural spline flow (NSF) to perform amortized Bayesian inference, producing posterior samples for the main source parameters in roughly one minute per event. For a representative MBHB whose merger occurs $\sim 15$ minutes after the end of the analyzed GW observation, the pipeline achieves pre-merger sky localizations of order $\sim 20~\mathrm{deg}^2$, recovers the same number of sky modes as a reference parallel-tempered Markov chain Monte Carlo (PTMCMC) analysis, and yields parameter uncertainties of comparable scale, while still operating within a practically useful pre-merger warning window. These results demonstrate that NSF-based inference can deliver accurate, near-real-time parameter estimation for space-borne MBHB GW signals, and that the resulting early-warning localizations are sufficiently precise to make rapid EM follow-up.

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 / 1 minor

Summary. The paper develops a fast, amortized Bayesian inference pipeline for pre-merger localization of massive black hole binaries (MBHBs) in a TianQin-like space-borne GW detector. It combines a learned embedding of the detector time series with a neural spline flow (NSF) to produce posterior samples for source parameters in roughly one minute per event. For one representative MBHB whose merger occurs ~15 minutes after the analyzed observation segment, the pipeline reports sky localizations of order ~20 deg², recovers the same number of sky modes as a reference PTMCMC sampler, and yields parameter uncertainties of comparable scale.

Significance. If the NSF-based approximation holds for low-SNR pre-merger segments and generalizes beyond the single tested event, the work would provide a practically useful tool for low-latency EM follow-up of MBHBs, addressing a key need for multi-messenger astronomy with future space-based detectors. The amortized approach is a strength for high-throughput analysis, though the limited validation scope restricts the assessed significance.

major comments (2)
  1. [Abstract] Abstract: the headline performance claim (~20 deg² localization, same sky-mode count and comparable uncertainties as PTMCMC for the representative MBHB) is obtained from a single event whose signal occupies only the final ~15 min before merger. No information is supplied on training dataset size, validation metrics, noise model details, or embedding learning procedure, so it is impossible to assess whether the learned density faithfully reproduces the true multimodal posterior shape at low SNR.
  2. [Results] The comparison to PTMCMC is presented only for one injection; without coverage diagnostics, calibration plots over an ensemble, or ablation studies on the embedding architecture, any systematic mismatch between the NSF and the actual likelihood surface would directly affect the reported mode count and uncertainty scales.
minor comments (1)
  1. [Title] The title uses 'pre-localization' without explicit definition; clarify that it refers to sky localization performed before merger.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to provide additional methodological details and broader validation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline performance claim (~20 deg² localization, same sky-mode count and comparable uncertainties as PTMCMC for the representative MBHB) is obtained from a single event whose signal occupies only the final ~15 min before merger. No information is supplied on training dataset size, validation metrics, noise model details, or embedding learning procedure, so it is impossible to assess whether the learned density faithfully reproduces the true multimodal posterior shape at low SNR.

    Authors: We thank the referee for this observation. The headline metrics are shown for a representative low-SNR pre-merger event (merger ~15 min after the segment) to demonstrate practical utility. Full details on the training set (10^5 injections drawn from astrophysical priors), validation metrics (coverage probabilities and KL divergence to PTMCMC), noise model (stationary Gaussian noise with the TianQin PSD), and embedding (CNN trained jointly with the NSF) appear in Sections 2 and 3. To improve accessibility we have revised the abstract to include a concise summary of the training and validation procedures. We have also added a short discussion of posterior fidelity at low SNR, confirming that the NSF recovers the same multimodal structure as PTMCMC for the reported case. revision: partial

  2. Referee: [Results] The comparison to PTMCMC is presented only for one injection; without coverage diagnostics, calibration plots over an ensemble, or ablation studies on the embedding architecture, any systematic mismatch between the NSF and the actual likelihood surface would directly affect the reported mode count and uncertainty scales.

    Authors: We agree that a single-injection comparison is insufficient to rule out systematic mismatches. The original text presented the PTMCMC run as an illustrative benchmark for the chosen event. In the revised manuscript we have added coverage diagnostics and calibration plots over an ensemble of 200 simulated events spanning SNR 5–50 and varied sky locations. These show that the NSF achieves nominal coverage (true parameters lie inside the 90 % credible region in 89 % of cases) and that sky-mode counts and uncertainty scales remain consistent with PTMCMC on average. We have also included ablation studies on embedding depth and preprocessing, confirming that the selected architecture minimizes deviations from the true likelihood surface. revision: yes

Circularity Check

0 steps flagged

No significant circularity in NSF-based pre-merger localization pipeline

full rationale

The paper presents an amortized Bayesian inference pipeline that trains a neural spline flow on simulated MBHB signals and validates its outputs (sky localizations of ~20 deg², sky mode count, and parameter uncertainties) for one representative event by direct numerical comparison to an independent PTMCMC sampler. No equations, fitted parameters, or self-citations reduce the reported results to quantities that are identical to the training inputs by construction. The central claims are empirical performance metrics of a computational method, not tautological derivations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The approach rests on standard assumptions from gravitational-wave data analysis and amortized inference; no new physical entities are introduced and free parameters are limited to typical neural-network hyperparameters.

free parameters (1)
  • neural spline flow hyperparameters
    Architecture depth, spline knots, and training schedule are chosen to fit the simulated signals; exact values not stated in abstract.
axioms (2)
  • domain assumption MBHB gravitational-wave signals are accurately described by general-relativity waveform models in the millihertz band.
    Required for the inference target; implicit in any GW parameter-estimation pipeline.
  • domain assumption Detector noise is stationary and Gaussian over the analyzed segment.
    Standard assumption enabling the likelihood used to train the flow.

pith-pipeline@v0.9.0 · 5607 in / 1522 out tokens · 87455 ms · 2026-05-08T02:16:28.405538+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

76 extracted references · 65 canonical work pages · 8 internal anchors

  1. [1]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]

    work page internal anchor Pith review arXiv 2016

  2. [2]

    Luo, L.-S

    J. Luo, L.-S. Chen, H.-Z. Duan, Y.-G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, et al., Tianqin: a space-borne gravitational wave detector, Classical and Quantum Gravity33, 035010 (2016)

    2016

  3. [3]

    Luo et al., The first round result from the TianQin- 1 satellite, Class

    J. Luo et al., The first round result from the TianQin- 1 satellite, Class. Quant. Grav.37, 185013 (2020), arXiv:2008.09534 [physics.ins-det]

    work page arXiv 2020

  4. [4]

    Amaro-Seoane et al., eLISA/NGO: Astrophysics and cosmology in the gravitational-wave millihertz regime, GW Notes6, 4 (2013), arXiv:1201.3621 [astro-ph.CO]

    P. Amaro-Seoane et al., eLISA/NGO: Astrophysics and cosmology in the gravitational-wave millihertz regime, GW Notes6, 4 (2013), arXiv:1201.3621 [astro-ph.CO]

    work page arXiv 2013

  5. [5]

    P. A. Seoane et al. (LISA), Astrophysics with the Laser Interferometer Space Antenna, Living Rev. Rel.26, 2 (2023), arXiv:2203.06016 [gr-qc]

    work page arXiv 2023

  6. [6]

    Wang et al., Science with the TianQin observa- tory: Preliminary results on massive black hole bina- ries, Phys

    H.-T. Wang et al., Science with the TianQin observa- tory: Preliminary results on massive black hole bina- ries, Phys. Rev. D100, 043003 (2019), arXiv:1902.04423 [astro-ph.HE]

    work page arXiv 2019

  7. [7]

    Bogdanovic, M

    T. Bogdanovic, M. C. Miller, and L. Blecha, Electromag- netic counterparts to massive black-hole mergers, Living Rev. Rel.25, 3 (2022), arXiv:2109.03262 [astro-ph.HE]

    work page arXiv 2022

  8. [8]

    Xin and Z

    C. Xin and Z. Haiman, Identifying the electromagnetic counterparts of LISA massive black hole binaries in archival LSST data, Mon. Not. Roy. Astron. Soc.533, 3164 (2024), arXiv:2403.18751 [astro-ph.HE]

    work page arXiv 2024

  9. [9]

    L. M. Krauth, J. Davelaar, Z. Haiman, J. R. Westernacher-Schneider, J. Zrake, and A. MacFadyen, Thermal X-ray signatures in late-stage unequal-mass massive black hole binary mergers, Mon. Not. Roy. As- tron. Soc.543, 2670 (2025), arXiv:2503.01494 [astro- ph.HE]

    work page arXiv 2025

  10. [10]

    Mangiagli, C

    A. Mangiagli, C. Caprini, M. Volonteri, S. Marsat, S. Ver- gani, N. Tamanini, and H. Inchausp´ e, Massive black hole binaries in LISA: Multimessenger prospects and electro- magnetic counterparts, Phys. Rev. D106, 103017 (2022), arXiv:2207.10678 [astro-ph.HE]

    work page arXiv 2022

  11. [11]

    Lai and D

    D. Lai and D. J. Mu˜ noz, Circumbinary Accretion: From Binary Stars to Massive Binary Black Holes, Ann. Rev. Astron. Astrophys.61, 517 (2023), arXiv:2211.00028 [astro-ph.HE]

    work page arXiv 2023

  12. [12]

    DeLaurentiis, Z

    S. DeLaurentiis, Z. Haiman, J. R. Westernacher- Schneider, L. M. Krauth, J. Davelaar, J. Zrake, and A. MacFadyen, Relativistic Binary Precession: Im- pact on Eccentric Massive Binary Black Hole Accre- tion and Hydrodynamics, Astrophys. J.980, 55 (2025), arXiv:2405.07897 [astro-ph.HE]

    work page arXiv 2025

  13. [13]

    L. M. Krauth, J. Davelaar, Z. Haiman, J. R. 19 1.5 3.0 [rad] 0.6 0.0 0.6 [rad] 0.19 0.20 0.21 0.22 [-] 885 900 915 930 tc [s] 5.4735.4765.4795.482log10 c[M ] 13.5 15.0 16.5 DL [Gpc] 1.5 3.0 [rad] 0.6 0.0 0.6 [rad] 0.19 0.20 0.21 0.22 [-] 885 900 915 930 tc [s] 13.5 15.0 16.5 DL [Gpc] 0.95 1.00 1.05 1.10 1.15 [rad] 0.95 1.00 1.05 1.10 1.15 [rad] NSF PTMCMC...

    work page arXiv 2023

  14. [14]

    Davelaar and Z

    J. Davelaar and Z. Haiman, Self-Lensing Flares from Black Hole Binaries: Observing Black Hole Shadows via Light Curve Tomography, Phys. Rev. Lett.128, 191101 (2022), arXiv:2112.05829 [astro-ph.HE]

    work page arXiv 2022

  15. [15]

    L. M. Krauth, J. Davelaar, Z. Haiman, J. R. Westernacher-Schneider, J. Zrake, and A. MacFadyen, Self-lensing flares from black hole binaries: General- relativistic ray tracing of circumbinary accretion simulations, Phys. Rev. D109, 103014 (2024), arXiv:2310.19766 [astro-ph.HE]

    work page arXiv 2024

  16. [16]

    Ingram, S

    A. Ingram, S. E. Motta, S. Aigrain, and A. Karastergiou, A self-lensing binary massive black hole interpretation of quasi-periodic eruptions, Mon. Not. Roy. Astron. Soc. 503, 1703 (2021), [Erratum: Mon.Not.Roy.Astron.Soc. 504, 5512 (2021)], arXiv:2103.00017 [astro-ph.HE]

    work page arXiv 2021

  17. [17]

    C. A. Dong-P´ aez, M. Volonteri, R. S. Beckmann, Y. Dubois, A. Mangiagli, M. Trebitsch, S. Vergani, and N. Webb, Multimessenger study of merging massive black holes in the OBELISK simulation: gravitational waves, electromagnetic counterparts, and their link to galaxy and black hole populations, Astron. Astrophys.676, A2 (2023), arXiv:2303.09569 [astro-ph.HE]

    work page arXiv 2023

  18. [18]

    Feng, H.-T

    W.-F. Feng, H.-T. Wang, X.-C. Hu, Y.-M. Hu, and 21 TABLE X. Comparison of sky-localization statistics between the NSF and PTMCMC samplers for the same event. Here Nmode is the number of sky modes identified by cluster- ing, ˆAtot,clustered is the total sky area obtained by summing over all clustered modes, and (∆λ m,∆β m, ˆAm) characterize the folded repr...

    work page arXiv 2019

  19. [19]

    Hoy and L

    C. Hoy and L. K. Nuttall, BILBY in space: Bayesian in- ference for transient gravitational-wave signals observed with LISA, Mon. Not. Roy. Astron. Soc.529, 3052 (2024), arXiv:2312.13039 [astro-ph.IM]

    work page arXiv 2024

  20. [20]

    N. J. Cornish, Heterodyned likelihood for rapid gravi- tational wave parameter inference, Phys. Rev. D104, 104054 (2021), arXiv:2109.02728 [gr-qc]

    work page arXiv 2021

  21. [21]

    Chen, X.-Y

    H.-Y. Chen, X.-Y. Lyu, E.-K. Li, and Y.-M. Hu, Near real-time gravitational wave data analysis of the massive black hole binary with TianQin, Sci. China Phys. Mech. Astron.67, 279512 (2024), arXiv:2309.06910 [gr-qc]

    work page arXiv 2024

  22. [22]

    M. L. Katz, N. Karnesis, N. Korsakova, J. R. Gair, and N. Stergioulas, Efficient GPU-accelerated multisource global fit pipeline for LISA data analysis, Phys. Rev. D 111, 024060 (2025), arXiv:2405.04690 [gr-qc]

    work page arXiv 2025

  23. [23]

    I. M. V´ ılchez and C. F. Sopuerta, Efficient Mas- sive Black Hole Binary parameter estimation for LISA using Sequential Neural Likelihood, JCAP04, 022, arXiv:2406.00565 [gr-qc]

    work page arXiv

  24. [24]

    M. Du, B. Liang, H. Wang, P. Xu, Z. Luo, and Y. Wu, Advancing space-based gravitational wave as- tronomy: Rapid parameter estimation via normalizing flows, Sci. China Phys. Mech. Astron.67, 230412 (2024), arXiv:2308.05510 [astro-ph.IM]

    work page arXiv 2024

  25. [25]

    Spadaro, J

    A. Spadaro, J. Gair, D. Gerosa, S. R. Green, R. Bus- cicchio, N. Gupte, R. Tenorio, S. Clyne, M. P¨ urrer, and N. Korsakova, Accurate and efficient simulation-based in- ference for massive black-hole binaries with LISA, arXiv e-prints (2026), arXiv:2603.20431 [astro-ph.HE]

    work page arXiv 2026

  26. [26]

    C. R. Weaving, L. K. Nuttall, I. W. Harry, S. Wu, and A. Nitz, Adapting the PyCBC pipeline to find and infer the properties of gravitational waves from massive black hole binaries in LISA, Class. Quant. Grav.41, 025006 (2024), arXiv:2306.16429 [astro-ph.IM]

    work page arXiv 2024

  27. [27]

    LISA Definition Study Report

    M. Colpi et al. (LISA), LISA Definition Study Report, arXiv e-prints (2024), arXiv:2402.07571 [astro-ph.CO]

    work page internal anchor Pith review arXiv 2024

  28. [28]

    Z. Luo, Y. Wang, Y. Wu, W. Hu, and G. Jin, The Taiji program: A concise overview, PTEP2021, 05A108 (2021)

    2021

  29. [29]

    Tinto, M

    M. Tinto, M. Vallisneri, and J. W. Armstrong, TDIR: Time-delay interferometric ranging for space-borne gravitational-wave detectors, Phys. Rev. D71, 041101 (2005), arXiv:gr-qc/0410122

    work page arXiv 2005

  30. [30]

    Tinto, J

    M. Tinto, J. W. Armstrong, and F. B. Estabrook, Dis- criminating a gravitational-wave background from instru- mental noise using time-delay interferometry, Classical and Quantum Gravity18, 4081 (2001)

    2001

  31. [31]

    Tinto and J

    M. Tinto and J. W. Armstrong, Cancellation of laser noise in an unequal-arm interferometer detector of grav- itational radiation, Phys. Rev. D59, 102003 (1999)

    1999

  32. [32]

    Wang, W.-L

    P.-P. Wang, W.-L. Qian, Y.-J. Tan, H.-Z. Wu, and C.- G. Shao, Geometric approach for the modified second generation time delay interferometry, Phys. Rev. D106, 024003 (2022), arXiv:2205.08709 [gr-qc]

    work page arXiv 2022

  33. [33]

    Ajith et al., Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins, Phys

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

    work page arXiv 2011

  34. [34]

    Marsat, J

    S. Marsat, J. G. Baker, and T. Dal Canton, Explor- ing the Bayesian parameter estimation of binary black holes with LISA, Phys. Rev. D103, 083011 (2021), arXiv:2003.00357 [gr-qc]

    work page arXiv 2021

  35. [35]

    First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries

    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, First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries, Phys. Rev. Lett.120, 161102 (2018), arXiv:1708.00404 [gr-qc]

    work page Pith review arXiv 2018

  36. [36]

    H.-Y. Chen, H. Wang, E.-K. Li, and Y.-M. Hu, Signal-to- noise ratio analytic formulae of the inspiral binary black holes in TianQin, Class. Quant. Grav.42, 155010 (2025), arXiv:2410.19401 [astro-ph.GA]

    work page arXiv 2025

  37. [37]

    Zhang, Y

    C. Zhang, Y. Gong, H. Liu, B. Wang, and C. Zhang, Sky localization of space-based gravitational wave detec- tors, Phys. Rev. D103, 103013 (2021), arXiv:2009.03476 [astro-ph.IM]

    work page arXiv 2021

  38. [38]

    Li et al., GWSpace: a multi-mission science data simulator for space-based gravitational wave detection, Class

    E.-K. Li et al., GWSpace: a multi-mission science data simulator for space-based gravitational wave detection, Class. Quant. Grav.42, 165005 (2025), arXiv:2309.15020 [gr-qc]

    work page arXiv 2025

  39. [39]

    Li et al., Gwspace (2023)

    E.-K. Li et al., Gwspace (2023)

    2023

  40. [40]

    L. S. Finn, Detection, measurement and gravitational radiation, Phys. Rev. D46, 5236 (1992), arXiv:gr- qc/9209010

    work page arXiv 1992

  41. [41]

    J. Skilling, Nested Sampling, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 24th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, American Institute of Physics Conference Series, Vol. 735, edited by R. Fischer, R. Preuss, and U. V. Toussaint (AIP, 2004) pp. 395–405

    2004

  42. [42]

    D. J. Earl and M. W. Deem, Parallel tempering: Theory, applications, and new perspectives, Physical Chemistry Chemical Physics (Incorporating Faraday Transactions) 7, 3910 (2005), arXiv:physics/0508111 [physics.comp- ph]

    work page arXiv 2005

  43. [43]

    Karnesis, M

    N. Karnesis, M. L. Katz, N. Korsakova, J. R. Gair, and N. Stergioulas, Eryn: a multipurpose sampler for Bayesian inference, Mon. Not. Roy. Astron. Soc.526, 4814 (2023), arXiv:2303.02164 [astro-ph.IM]

    work page arXiv 2023

  44. [44]

    H. G. Katzgraber, S. Trebst, D. A. Huse, and M. Troyer, Feedback-optimized parallel tempering Monte Carlo, Journal of Statistical Mechanics: Theory and Ex- periment2006, 03018 (2006), arXiv:cond-mat/0602085 [cond-mat.other]

    work page arXiv 2006

  45. [45]

    W. D. Vousden, W. M. Farr, and I. Mandel, Dynamic temperature selection for parallel tempering in Markov 22 chain Monte Carlo simulations, Mon. Not. R. Astron. Soc.455, 1919 (2016), arXiv:1501.05823 [astro-ph.IM]

    work page arXiv 1919

  46. [46]

    Zackay, L

    B. Zackay, L. Dai, and T. Venumadhav, Relative Bin- ning and Fast Likelihood Evaluation for Gravitational Wave Parameter Estimation, arXiv e-prints (2018), arXiv:1806.08792 [astro-ph.IM]

    work page arXiv 2018

  47. [47]

    Leslie, L

    N. Leslie, L. Dai, and G. Pratten, Mode-by-mode rel- ative binning: Fast likelihood estimation for gravita- tional waveforms with spin-orbit precession and mul- tiple harmonics, Phys. Rev. D104, 123030 (2021), arXiv:2109.09872 [astro-ph.IM]

    work page arXiv 2021

  48. [48]

    Narola, J

    H. Narola, J. Janquart, Q. Meijer, K. Haris, and C. Van Den Broeck, Gravitational-wave parameter estimation with relative binning: Inclusion of higher-order modes and precession, and applications to lensing and third- generation detectors, Phys. Rev. D110, 084085 (2024), arXiv:2308.12140 [gr-qc]

    work page arXiv 2024

  49. [49]

    Proceedings of the National Academy of Sciences of the United States of America , number =

    P. Marjoram, J. Molitor, V. Plagnol, and S. Tavar´ e, Markov chain monte carlo with- out likelihoods, Proceedings of the National Academy of Sciences100, 15324 (2003), https://www.pnas.org/doi/pdf/10.1073/pnas.0306899100

    work page doi:10.1073/pnas.0306899100 2003

  50. [50]

    Cranmer, J

    K. Cranmer, J. Brehmer, and G. Louppe, The frontier of simulation-based inference, Proceedings of the National Academy of Science117, 30055 (2020), arXiv:1911.01429 [stat.ML]

    work page arXiv 2020

  51. [51]

    Lueckmann, J

    J.-M. Lueckmann, J. Boelts, D. S. Greenberg, P. J. Gon¸ calves, and J. H. Macke, Benchmarking Simulation- Based Inference, arXiv e-prints , arXiv:2101.04653 (2021), arXiv:2101.04653 [stat.ML]

    work page arXiv 2021

  52. [52]

    D. P. Kingma and M. Welling, Auto-Encoding Varia- tional Bayes, arXiv e-prints , arXiv:1312.6114 (2013), arXiv:1312.6114 [stat.ML]

    work page internal anchor Pith review arXiv 2013

  53. [53]

    Variational Inference with Normalizing Flows

    D. Jimenez Rezende and S. Mohamed, Variational Inference with Normalizing Flows, arXiv e-prints , arXiv:1505.05770 (2015), arXiv:1505.05770 [stat.ML]

    work page Pith review arXiv 2015

  54. [54]

    Hyv¨ arinen and P

    A. Hyv¨ arinen and P. Dayan, Estimation of non- normalized statistical models by score matching., Journal of Machine Learning Research6(2005)

    2005

  55. [55]

    Prangle, Summary Statistics in Approximate Bayesian Computation, arXiv e-prints , arXiv:1512.05633 (2015), arXiv:1512.05633 [stat.CO]

    D. Prangle, Summary Statistics in Approximate Bayesian Computation, arXiv e-prints , arXiv:1512.05633 (2015), arXiv:1512.05633 [stat.CO]

    work page arXiv 2015

  56. [56]

    Normalizing Flows: An Introduction and Review of Current Methods,

    I. Kobyzev, S. J. D. Prince, and M. A. Brubaker, Nor- malizing Flows: An Introduction and Review of Cur- rent Methods, arXiv e-prints , arXiv:1908.09257 (2019), arXiv:1908.09257 [stat.ML]

    work page arXiv 1908

  57. [57]

    Durkan, A

    C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios, Neural Spline Flows, arXiv e-prints , arXiv:1906.04032 (2019), arXiv:1906.04032 [stat.ML]

    work page arXiv 1906

  58. [58]

    L. Dinh, J. Sohl-Dickstein, and S. Bengio, Den- sity estimation using Real NVP, arXiv e-prints , arXiv:1605.08803 (2016), arXiv:1605.08803 [cs.LG]

    work page internal anchor Pith review arXiv 2016

  59. [59]

    M. J. Williams, jmcginn, federicostak, and J. Veitch, uof- gravity/glasflow: v0.4.1 (2024)

    2024

  60. [60]

    Ruan and Z.-K

    W.-H. Ruan and Z.-K. Guo, Premerger detection of mas- sive black hole binaries using deep learning, Phys. Rev. D109, 123031 (2024), arXiv:2402.16282 [astro-ph.IM]

    work page arXiv 2024

  61. [61]

    Zhang, N

    X.-T. Zhang, N. Korsakova, M. L. Chan, C. Messenger, and Y.-M. Hu, Searching for gravitational waves from stellar-mass binary black holes early inspiral, Phys. Rev. D110, 103034 (2024), arXiv:2406.07336 [astro-ph.SR]

    work page arXiv 2024

  62. [62]

    Going Deeper with Convolutions

    C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabi- novich, Going Deeper with Convolutions, arXiv e-prints , arXiv:1409.4842 (2014), arXiv:1409.4842 [cs.CV]

    work page Pith review arXiv 2014

  63. [63]

    Zhang, C

    X.-T. Zhang, C. Messenger, N. Korsakova, M. L. Chan, Y.-M. Hu, and J.-d. Zhang, Detecting gravitational waves from extreme mass ratio inspirals using convolutional neural networks, Phys. Rev. D105, 123027 (2022), arXiv:2202.07158 [astro-ph.HE]

    work page arXiv 2022

  64. [64]

    K. He, X. Zhang, S. Ren, and J. Sun, Deep Residual Learning for Image Recognition, in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016) p. 1, arXiv:1512.03385 [cs.CV]

    work page internal anchor Pith review arXiv 2016

  65. [65]

    K. M. G´ orski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelman, HEALPix - A Framework for high resolution discretization, and fast analysis of data distributed on the sphere, Astrophys. J. 622, 759 (2005), arXiv:astro-ph/0409513

    work page internal anchor Pith review arXiv 2005

  66. [66]

    NASA GCN Team, GCN – Missions – LIGO/Virgo/KAGRA,https://gcn.nasa.gov/ missions/lvk(2023), accessed 23 February 2026

    2023

  67. [67]

    LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, LIGO/Virgo/KAGRA Public Alerts User Guide,https://emfollow.docs.ligo.org/ userguide(2023), public documentation on GW alert contents and timeline

    2023

  68. [68]

    S. S. Chaudhary et al., Low-latency gravitational wave alert products and their performance at the time of the fourth LIGO-Virgo-KAGRA observing run, Proc. Nat. Acad. Sci.121, e2316474121 (2024), arXiv:2308.04545 [astro-ph.HE]

    work page arXiv 2024

  69. [69]

    LSST Science Collaboration, P. A. Abell, J. Allison, S. F. Anderson, J. R. Andrew, J. R. P. Angel, L. Ar- mus, D. Arnett, S. J. Asztalos, T. S. Axelrod, S. Bai- ley, D. R. Ballantyne, J. R. Bankert, W. A. Barkhouse, J. D. Barr, L. F. Barrientos, A. J. Barth, J. G. Bartlett, A. C. Becker, J. Becla, T. C. Beers, J. P. Bernstein, R. Biswas, M. R. Blanton, J....

    work page Pith review arXiv 2009

  70. [70]

    E. C. Bellm, S. R. Kulkarni, M. J. Graham, R. Dekany, R. M. Smith, R. Riddle, F. J. Masci, G. Helou, T. A. Prince, S. M. Adams, C. Barbarino, T. Barlow, J. Bauer, R. Beck, J. Belicki, R. Biswas, N. Blagorodnova, D. Bodewits, B. Bolin, V. Brinnel, T. Brooke, B. Bue, M. Bulla, R. Burruss, S. B. Cenko, C.-K. Chang, A. Con- nolly, M. Coughlin, J. Cromer, V. C...

    work page Pith review arXiv 2019

  71. [71]

    Kaiser, W

    N. Kaiser, W. Burgett, K. Chambers, L. Den- neau, J. Heasley, R. Jedicke, E. Magnier, J. Morgan, P. Onaka, and J. Tonry, The Pan- STARRS wide-field optical/NIR imaging survey, in Ground-based and Airborne Telescopes III, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7733, edited by L. M. Stepp, R. Gilmozzi, and H. J. Ha...

    2010

  72. [72]

    K. C. Chambers, E. A. Magnier, N. Metcalfe, H. A. Flewelling, M. E. Huber, C. Z. Waters, L. Denneau, P. W. Draper, D. Farrow, D. P. Finkbeiner, C. Holmberg, J. Koppenhoefer, P. A. Price, A. Rest, R. P. Saglia, E. F. Schlafly, S. J. Smartt, W. Sweeney, R. J. Wainscoat, W. S. Burgett, S. Chastel, T. Grav, J. N. Heasley, K. W. Hodapp, R. Jedicke, N. Kaiser, ...

    work page internal anchor Pith review arXiv 2016

  73. [73]

    The Hot and Energetic Universe: A White Paper presenting the science theme motivating the Athena+ mission

    K. Nandra, D. Barret, X. Barcons, A. Fabian, J.-W. den Herder, L. Piro, M. Watson, C. Adami, J. Aird, J. M. Afonso, D. Alexander, C. Argiroffi, L. Amati, M. Ar- naud, J.-L. Atteia, M. Audard, C. Badenes, J. Ballet, L. Ballo, A. Bamba, A. Bhardwaj, E. Stefano Battis- telli, W. Becker, M. De Becker, E. Behar, S. Bianchi, V. Biffi, L. Bˆ ırzan, F. Bocchino, ...

    work page Pith review arXiv 2013

  74. [74]

    Houba, G

    N. Houba, G. Giarda, and L. Speri, SlotFlow: Amor- tized Trans-Dimensional Inference with Slot-Based Nor- malizing Flows, arXiv e-prints (2025), arXiv:2511.23228 [astro-ph.IM]

    work page arXiv 2025

  75. [75]

    Branchesi, M

    M. Branchesi et al., Science with the Einstein Tele- scope: a comparison of different designs, JCAP07, 068, arXiv:2303.15923 [gr-qc]

    work page arXiv

  76. [76]

    A Horizon Study for Cosmic Explorer: Science, Observatories, and Community

    M. Evans et al., A Horizon Study for Cosmic Explorer: Science, Observatories, and Community, arXiv e-prints (2021), arXiv:2109.09882 [astro-ph.IM]

    work page internal anchor Pith review arXiv 2021