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A GPU port of the standard gravitational-wave sampler runs 20-40x faster

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A GPU implementation of the bilby/dynesty acceptance-walk nested sampler recovers statistically equivalent posteriors and evidences with large core-hour speedups.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A genuinely useful GPU port of the bilby/dynesty acceptance-walk sampler with solid statistical validation, but the headline '20-40x' speedups are CPU-core-hour throughput numbers, not wall-clock speedups; real wall-clock gains are about 2-3x. the 3 major comments →

arxiv 2509.04336 v1 pith:MKGUWNHT submitted 2025-09-04 gr-qc astro-ph.HEastro-ph.IM

Gravitational-wave inference at GPU speed: A bilby-like nested sampling kernel within blackjax-ns

Metha Prathaban , David Yallup , James Alvey , Ming Yang , Will Templeton , Will Handley This is my paper
classification gr-qc astro-ph.HEastro-ph.IM
keywords gravitational-wave astronomynested samplingGPU accelerationBayesian parameter estimationmodel selectionbinary black holesdifferential evolution MCMCacceptance-walk sampler
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper claims that the acceptance-walk nested sampling kernel used by the standard gravitational-wave inference pipeline can be transplanted almost unchanged into a GPU-native vectorized nested sampling framework, and that the result reproduces the CPU sampler's posteriors and evidences while running 20-40 times faster on aligned-spin binary black hole analyses. The authors re-implement the same differential-evolution proposal and walk-length adaptation logic, changing only what the GPU architecture forces: points are removed and replaced in batches rather than one at a time, and walk-length tuning is done per batch instead of per iteration. To keep the comparison fair, they compensate for the saw-tooth live-point pattern that batch processing introduces by using about 1.4 times as many live points on the GPU, a factor derived from equating expected prior-volume shrinkage. If the claim holds, the speedup is attributable to hardware parallelization alone, giving the field a clean benchmark for judging genuinely new sampling algorithms. The work matters because gravitational-wave parameter estimation and model selection are currently expensive and will only get more so with future detectors.

Core claim

The paper establishes that a batched, GPU-vectorized implementation of the bilby+dynesty acceptance-walk nested sampler yields statistically identical posterior distributions and log-evidence estimates to the original sequential CPU implementation for aligned-spin binary black hole signals (IMRPhenomD, three-detector O4 noise), with wall-clock speedups of 20-40x and cost reductions of about 1.5-2.5x. The central technical fix is Eq. 7: setting the GPU live-point count to 2 ln(2) ≈ 1.4 times the CPU count, with batch size k = 0.5 n_GPU, so the expected prior-volume compression per iteration matches despite the saw-tooth live-point pattern. Validation includes a 100-injection PP plot showing w

What carries the argument

The carrying object is the acceptance-walk inner kernel: a differential-evolution MCMC walk started from the deleted live point, in unit hypercube space, accepting steps that keep likelihood above the current threshold, with the walk length adaptively tuned to hit a target number of accepted steps (default 60). The GPU adaptation replaces single-point deletion with batch deletion of k points, forcing: (i) a fixed walk length across the batch with tuning performed on the mean acceptance rate; (ii) a smoothing 'delay' parameter rescaled as a function of batch size; and (iii) a live-point count inflated by 2 ln(2) ≈ 1.4 to cancel the saw-tooth prior-volume deficit. That ratio identity is what m

Load-bearing premise

That setting the GPU live-point count to 1.4 times the CPU count (with batch size half of that) and tuning walk lengths once per batch with an adjusted smoothing factor gives the same effective live points and chain decorrelation as bilby's per-iteration tuning; if not, the two samplers are not being compared on equal terms and the speedup numbers lose their benchmark meaning.

What would settle it

Run a set of injections at several batch sizes (num_delete ≈ 0.1, 0.5, and 0.9 times n_live), each time scaling n_GPU by the corresponding integral-compression formula, and compare the resulting posterior and log-Z distributions to bilby's. If the evidence scatter and effective number of iterations shift systematically with batch size, the compensation identity is only tuned to the recommended batch size rather than generally true.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the kernel is truly functionally equivalent, bilby users can switch to the GPU implementation without re-validating their physical analyses: posteriors and evidences are the same objects.
  • The 20-40x speedup at fixed hardware cost translates to roughly 2x cost savings on current cloud rates, and the advantage should grow as GPU prices fall relative to CPUs.
  • The framework provides a hardware-only baseline: any future GPU sampler that beats it must be credited with algorithmic improvement, not just parallelization.
  • The same relative speedups are expected to carry over to more expensive waveforms, such as precessing and higher-order-mode models, once GPU-native implementations exist, with the caveat that long-duration likelihoods can saturate the GPU and reintroduce serial scaling.
  • The batched architecture is naturally compatible with normalizing-flow proposals, opening a route to hybrid machine-learning-accelerated nested sampling.

Where Pith is reading between the lines

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

  • The 2 ln(2) compensation is derived for the specific batch size k = 0.5 n_GPU; using other batch sizes would require re-deriving the factor, and the paper's injection study only validates the calibrated setting.
  • The equivalence claim is tested on aligned-spin BBH with IMRPhenomD; for higher-dimensional precessing models the approximation that batch-level tuning reproduces per-iteration decorrelation may be strained, so the speedup figure should not be extrapolated without a dedicated test.
  • A sharper check of the like-for-like claim would be to compare evidence uncertainties across repeated runs with random seeds: if the effective live points really match, the scatter in log Z should match bilby's, not just the mean.
  • The reported speedup on the 8-second signal already shows the GPU saturating; extending this work to third-generation detectors will likely require compressed likelihoods (heterodyning) or multi-GPU decomposition before the full 20-40x carries over.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents a GPU-accelerated implementation of the bilby/dynesty 'acceptance-walk' nested-sampling kernel within the blackjax-ns vectorized framework. The authors adapt the sequential CPU algorithm by deleting batches of k live points, fixing the MCMC walk length within a batch and tuning it at batch level, and using the ripple GPU waveform generator. They validate against bilby+dynesty on a 4s BBH signal, an 8s signal, and a 100-injection study, reporting well-calibrated PP plots and consistent log-evidences, with similar numbers of likelihood evaluations and acceptance rates. They claim typical speedups of 20-40x and cost reductions of 1.5-2.5x.

Significance. If the performance claims are corrected, this is a useful contribution: a GPU-native re-implementation of the community-standard sampler, with public code/data, explicit validation of posterior calibration and evidence, and an attempt to decompose speedups into likelihood-level and sampler-level contributions. The statistical validation is a strength (PP p=0.913; KS p=0.062 on evidence errors). However, the headline speedup figure is not computed on a like-for-like basis and is presented as a wall-clock speedup when it is actually a CPU-core-hour throughput speedup.

major comments (3)
  1. [§4.1.1, Table 3, §4.2, §4.4, Fig. 8, Abstract, §5] The reported 'speedup' is computed as CPU-core-hours divided by GPU-wall-clock-hours, not wall-clock-to-wall-clock. In §4.1.1, bilby took 2.99 h on 16 cores (47.8 CPU-h) and blackjax-ns took 1.25 h on one GPU: the wall-clock speedup is 2.4×, not 38×. In §4.2, the mean is 26.3 CPU-h = 1.64 h wall-clock vs 0.82 h GPU, i.e. 2.0×, not 32×. In §4.4, 167.2 CPU-h = 10.45 h wall-clock vs 4.55 h, i.e. 2.3×, not 37×. Figure 8's caption explicitly multiplies CPU wall-time by 16, and the cost-reduction numbers quoted in the text (2.4×, 2.0×, 2.3×) are the honest wall-clock comparisons. The abstract and §5 claim 'wall-time speedups of 20–40×'; this is an apples-to-oranges comparison. Please correct the metric throughout, or clearly reframe the claims as CPU-core-hour throughput speedups.
  2. [§4.3] The experiment designed to isolate intra-likelihood GPU acceleration uses bilby with its standard CPU likelihood as the baseline, while the GPU run uses ripple for the same waveform. Without benchmarking the same waveform code on the CPU and GPU, the 3.3× attributed to 'intra-likelihood' parallelization conflates the waveform-library implementation with the hardware shift. This weakens the claim that the gains are attributable solely to the architectural shift. A controlled comparison (e.g., a vectorized CPU version of ripple) or a clear qualification is needed.
  3. [§3.2.1, Eqs (3)–(7)] The derivation equating effective live-point numbers has sign errors (log-volume shrinkages are negative) and the integral approximation is not justified for the batch-deletion scheme described in §3.1. More importantly, the 'like-for-like' claim also assumes that batch-level walk-length tuning with the modified delay produces the same chain decorrelation as bilby's per-iteration tuning. Appendix B shows similar likelihood-evaluation counts and acceptance rates, but not the autocorrelation of the chains. Given the acknowledged 'underestimation of the error bars' and the marginal KS p=0.062 in Fig. 10, the paper should provide a direct decorrelation diagnostic (e.g., effective sample size per likelihood evaluation) or temper the claim that the samplers are statistically identical.
minor comments (5)
  1. [§3.2.1, Eqs (3)–(5)] The minus signs in the expected log-volume shrinkages are omitted; as written the equations give positive log X, which is confusing. Please add a remark that the comparison is between magnitudes.
  2. [Figure 11 caption vs §4.4] Figure 11 caption states a 'wall-time speedup of 46×' for the 8s signal, while §4.4 text says 37×; reconcile the discrepancy.
  3. [§4.2, Fig. 8] The 'mean speedup of 32×' following Fig. 8 should be labelled as core-hour throughput speedup, consistent with the figure caption.
  4. [§3.2] The modified 'delay' parameter is not defined; please give the exact formula used in the tuning adaptation.
  5. [Figure 11 label] The label 'blackjax ns + dynesty kernel' is misleading; the kernel is implemented in blackjax-ns and is not dynesty itself.

Circularity Check

0 steps flagged

No significant circularity: the central validation is against the external bilby+dynesty benchmark, and the paper's analytic adjustments are independent of the claimed result.

full rationale

The paper's central claim is that its GPU implementation of the acceptance-walk nested sampling kernel recovers statistically identical posteriors and evidences to the CPU-based bilby+dynesty pipeline, while being faster. This claim is validated against an external community-standard implementation using identical likelihoods, priors, and termination criteria (Sections 4.1.1, 4.2, 4.4; Figures 1, 4, 7, 10, 12), not against the paper's own prior results. The speedup numbers are benchmark measurements, not quantities derived from their own definition; the skeptical concern that CPU core-hours are compared to GPU wall-clock hours is a benchmarking-validity or correctness issue, not a circularity. The n_GPU = 2 ln(2) * n_CPU relation (Eq. 7) follows from Skilling's expected log prior-volume shrinkage (Eq. 3) together with the chosen batch fraction k = 0.5 * n_GPU; it is an analytic adjustment made before comparison, not a parameter fitted to the benchmark outputs. The similar iteration counts seen in Figure 3 are presented as a consistency check of that pre-registered scaling, not as the origin of the formula. Likewise, the delay-parameter tuning is a pre-comparison configuration choice intended to match accept-step statistics; it does not by construction force the posterior and evidence agreement, which remains a nontrivial empirical outcome. Self-citations to Yallup et al. (2025a) and to the authors' data/code repositories supply framework infrastructure and reproducibility, but the correctness of that infrastructure is independently demonstrated in this paper by agreement with bilby+dynesty. No load-bearing circular step is present.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard nested sampling theory and on the assumption that batch-level tuning preserves the sampling behavior of the sequential algorithm. The only hand-tuned numerical inputs are the delay parameter and batch size. No new physical entities are introduced.

free parameters (2)
  • delay = Not given numerically; adjusted as a function of batch size
    The smoothing factor in the walk-length tuning formula is modified from the bilby default to account for batch-level tuning (Section 3.2). The value is chosen by the authors to match bilby's acceptance-step behavior, as validated in Appendix B.
  • num_delete (batch size k) = 700 (0.5 * n_live) in all comparative runs
    The batch size is user-configurable and set to 0.5 * n_live, described as a good balance of parallel efficiency and sampling accuracy (Section 3.2, citing Yallup et al. 2025a). This choice affects the saw-tooth correction and the speedup measurements.
axioms (4)
  • standard math Expected log prior volume shrinkage formula E[log X_k] = sum_i 1/n_i (Eq. 3)
    Used in Section 3.2.1 to derive the n_GPU correction factor; sourced from Skilling (2006), Higson et al. (2019), Hu et al. (2024).
  • domain assumption The frequency-domain Gaussian likelihood with known noise PSD and IMRPhenomD waveform is a valid model for the simulated signals
    Used throughout Sections 3.3 and 4; the GPU waveform from ripple is assumed to be numerically faithful to the CPU waveform implementation.
  • domain assumption Batch-level adaptive walk-length tuning with adjusted delay produces chains as decorrelated as bilby's per-iteration tuning
    Section 3.1 and Appendix B argue that the mean acceptance rate over a batch, used to tune the fixed walk length, yields similar acceptance rates and likelihood evaluations to bilby. This is load-bearing for the 'functionally equivalent' claim.
  • domain assumption The bilby+dynesty analyses used as reference are correctly configured and their results are a valid ground truth
    The equivalence claim is based on matching bilby+dynesty outputs; any configuration error in the CPU reference would propagate to the validation.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Gravitational-wave inference at GPU speed: A bilby-like nested sampling kernel within blackjax-ns." pith.science (2026). https://pith.science/paper/MKGUWNHT

@misc{pith2026250904336,
  author       = {Pith},
  title        = {Pith review of: Gravitational-wave inference at GPU speed: A bilby-like nested sampling kernel within blackjax-ns},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MKGUWNHT}},
  note         = {Machine review of arXiv:2509.04336}
}
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read the original abstract

We present a GPU-accelerated implementation of the gravitational-wave Bayesian inference pipeline for parameter estimation and model comparison. Specifically, we implement the `acceptance-walk' sampling method, a cornerstone algorithm for gravitational-wave inference within the bilby and dynesty framework. By integrating this trusted kernel with the vectorized blackjax-ns framework, we achieve typical speedups of 20-40x for aligned spin binary black hole analyses, while recovering posteriors and evidences that are statistically identical to the original CPU implementation. This faithful re-implementation of a community-standard algorithm establishes a foundational benchmark for gravitational-wave inference. It quantifies the performance gains attributable solely to the architectural shift to GPUs, creating a vital reference against which future parallel sampling algorithms can be rigorously assessed. This allows for a clear distinction between algorithmic innovation and the inherent speedup from hardware. Our work provides a validated community tool for performing GPU-accelerated nested sampling in gravitational-wave data analyses.

Figures

Figures reproduced from arXiv: 2509.04336 by David Yallup, James Alvey, Metha Prathaban, Ming Yang, Will Handley, Will Templeton.

Figure 1
Figure 1. Figure 1: Recovered posteriors for the 4s signal. The posteriors are in excellent agreement with each other, demonstrating that the blackjax-ns implementation with our custom kernel is functionally equivalent to the bilby + dynesty implementation. straint, L > Lmin, where Lmin is now the maximum likelihood of the discarded batch. This reformulation transforms the computationally intensive task of sample generation f… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the number of live points in the sequential CPU and batched GPU implementations. Although the nominal number of live points used in blackjax-ns is higher than in bilby, the saw-tooth pattern means that the effective number of live points is the same. Here, we use a batch size of 𝑘 = 0.5 × 𝑛live. MNRAS 000, 1–12 (2025) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the sample weights for each dead point for the se￾quential CPU and batched GPU implementations. The weights are calculated using the prior volumes enclosed between successive dead points and the likelihoods. The shapes are similar, and both implementations enter the bulk of the posterior distribution at similar iterations, indiciating that setting the number of live points in blackjax-ns to 1… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the log evidence for the 4s signal. The results are in excellent agreement, demonstrating the robustness of the blackjax-ns implementation in recovering the same posteriors and evidence as the bilby implementation. This unifies parameter estimation and evidence evaluation into a single GPU-accelerated framework [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of the network signal-to-noise ratios (SNR) for the injected signals. 0 10000 20000 30000 Iteration 0 50 100 150 Accepted Steps CPU GPU [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the accepted number of steps per iteration for the sequential CPU and batched GPU analyses of the first signal from the injection study. We adapt our ‘delay’ parameter from the tuning formula such that we obtain similar accepted steps for the two implementations. The blackjax-ns implementation can only perform tuning every num_delete iterations, so we tune the chain length more aggressively. … view at source ↗
Figure 9
Figure 9. Figure 9: The cost reductions for all 100 events in the injection study. Al￾though the runtime speedups are significant, the more honest and fair com￾parison is of the relative costs of the two sets of analyses, since GPUs are more expensive than CPUs. We use the commercial on-demand rates for a 16-core CPU instance and an L4 GPU instance at the time of this work, and compare the cost savings obtained from using our… view at source ↗
Figure 10
Figure 10. Figure 10: The log evidence difference between the blackjax-ns and bilby+dynesty samplers for each injection in the study. For each esti￾mate, we take the mean log evidence estimated by bilby to be the reference value, and subtract the bilby estimates from the log evidences calculated by blackjax-ns. The error bars represent 1𝜎 confidence intervals for these differences. There appears to be some underestimation of t… view at source ↗
Figure 11
Figure 11. Figure 11: Recovered posterior distributions for the 8s simulated signal, comparing our GPU-based blackjax-ns sampler with the CPU-based bilby sampler. The injected values are marked by black lines. The strong statistical agreement confirms the validity of our implementation for longer-duration signals. The GPU implementation provided a wall-time speedup of 46× and a cost reduction of 2.9×. 33.8 34.0 34.2 34.4 34.6 … view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of the recovered log-evidence (𝑍) for the 8s signal. The results from both the bilby and blackjax-ns frameworks are consistent within their estimated numerical uncertainties. frequency bin, the likelihood evaluation time would be independent of signal duration. In such a scenario, the total runtime would be dictated primarily by the number of likelihood evaluations needed for convergence. In th… view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

60 extracted references · 15 canonical work pages · cited by 6 Pith papers · 1 internal anchor

  1. [1]

    P., et al., 2016, @doi [Phys

    Abbott B. P., et al., 2016, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.116.061102 , 116, 061102

    doi:10.1103/physrevlett.116.061102 2016

  2. [2]

    P., et al., 2017a, @doi [Phys

    Abbott B. P., et al., 2017a, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.119.161101 , 119, 161101

    doi:10.1103/physrevlett.119.161101

  3. [3]

    P., et al., 2017b, @doi [Nature] 10.1038/nature24471 , 551, 85

    Abbott B. P., et al., 2017b, @doi [Nature] 10.1038/nature24471 , 551, 85

    doi:10.1038/nature24471

  4. [4]

    P., et al., 2019, @doi [Phys

    Abbott B. P., et al., 2019, @doi [Phys. Rev. X] 10.1103/PhysRevX.9.031040 , 9, 031040

    doi:10.1103/physrevx.9.031040 2019

  5. [5]

    P., et al., 2020a, @doi [Living Rev

    Abbott B. P., et al., 2020a, @doi [Living Rev. Rel.] 10.1007/s41114-020-00026-9 , 23, 3

    doi:10.1007/s41114-020-00026-9

  6. [6]

    P., et al., 2020b, @doi [Classical and Quantum Gravity] 10.1088/1361-6382/ab685e , 37, 055002

    Abbott B. P., et al., 2020b, @doi [Classical and Quantum Gravity] 10.1088/1361-6382/ab685e , 37, 055002

    doi:10.1088/1361-6382/ab685e

  7. [7]

    Abbott R., et al., 2021, @doi [Phys. Rev. D] 10.1103/PhysRevD.103.122002 , 103, 122002

    doi:10.1103/physrevd.103.122002 2021

  8. [8]

    Abbott R., et al., 2023a, @doi [Phys. Rev. X] 10.1103/PhysRevX.13.011048 , 13, 011048

    doi:10.1103/physrevx.13.011048

  9. [9]

    Abbott R., et al., 2023b, @doi [Phys. Rev. X] 10.1103/PhysRevX.13.041039 , 13, 041039

    doi:10.1103/physrevx.13.041039

  10. [10]

    Abbott R., et al., 2024, @doi [Phys. Rev. D] 10.1103/PhysRevD.109.022001 , 109, 022001

    doi:10.1103/physrevd.109.022001 2024

  11. [11]

    Acernese F., et al., 2014, Classical and Quantum Gravity, 32, 024001

    work page 2014

  12. [12]

    Ashton G., et al., 2019, @doi [Astrophys. J. Suppl.] 10.3847/1538-4365/ab06fc , 241, 27

    doi:10.3847/1538-4365/ab06fc 2019

  13. [13]

    2022, @doi [Nature Reviews Methods Primers] 10.1038/s43586-022-00121-x , 2, 39

    Ashton G., Bernstein N., Buchner J., et al. 2022, @doi [Nature Reviews Methods Primers] 10.1038/s43586-022-00121-x , 2, 39

    doi:10.1038/s43586-022-00121-x 2022

  14. [14]

    M., Lasky P

    Baker A. M., Lasky P. D., Thrane E., Golomb J., 2025, Significant challenges for astrophysical inference with next-generation gravitational-wave observatories ( @eprint arXiv 2503.04073 )

    work page arXiv 2025

  15. [15]

    Bayes T., 1763, @doi [Philosophical Transactions of the Royal Society of London] 10.1098/rstl.1763.0053 , https://ui.adsabs.harvard.edu/abs/1763RSPT...53..370B 53, 370

    arXiv

  16. [16]

    M., Capano C

    Biwer C. M., Capano C. D., De S., Cabero M., Brown D. A., Nitz A. H., Raymond V., 2019, @doi [Publications of the Astronomical Society of the Pacific] 10.1088/1538-3873/aaef0b , https://ui.adsabs.harvard.edu/abs/2019PASP..131b4503B 131, 024503

    doi:10.1088/1538-3873/aaef0b 2019

  17. [17]

    Bradbury J., et al., 2018, JAX : composable transformations of P ython+ N um P y programs, http://github.com/google/jax

    2018

  18. [18]

    Branchesi M., et al., 2023, @doi [Journal of Cosmology and Astroparticle Physics] 10.1088/1475-7516/2023/07/068 , 2023, 068

    doi:10.1088/1475-7516/2023/07/068 2023

  19. [19]

    Buchner J., 2023, @doi [Statistics Surveys] 10.1214/23-SS144 , 17, 169

    doi:10.1214/23-ss144 2023

  20. [20]

    Cabezas A., Corenflos A., Lao J., Louf R., 2024, BlackJAX: Composable B ayesian inference in JAX ( @eprint arXiv 2402.10797 )

    Pith/arXiv arXiv 2024

  21. [21]

    Christensen N., Meyer R., 2022, @doi [Rev. Mod. Phys.] 10.1103/RevModPhys.94.025001 , 94, 025001

    doi:10.1103/revmodphys.94.025001 2022

  22. [22]

    J., 2013, Fast Fisher Matrices and Lazy Likelihoods ( @eprint arXiv 1007.4820 ), https://arxiv.org/abs/1007.4820

    Cornish N. J., 2013, Fast Fisher Matrices and Lazy Likelihoods ( @eprint arXiv 1007.4820 ), https://arxiv.org/abs/1007.4820

    Pith/arXiv arXiv 2013

  23. [23]

    Dau H.-D., Chopin N., 2021, Waste-free Sequential Monte Carlo ( @eprint arXiv 2011.02328 ), https://arxiv.org/abs/2011.02328

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  24. [24]

    Edwards T. D. P., Wong K. W. K., Lam K. K. H., Coogan A., Foreman-Mackey D., Isi M., Zimmerman A., 2024, @doi [Phys. Rev. D] 10.1103/PhysRevD.110.064028 , 110, 064028

    doi:10.1103/physrevd.110.064028 2024

  25. [25]

    J., Hobson M

    Handley W. J., Hobson M. P., Lasenby A. N., 2015, @doi [Mon. Not. Roy. Astron. Soc.] 10.1093/mnras/stv1911 , 453, 4385

    doi:10.1093/mnras/stv1911 2015

  26. [26]

    W., Goggans P

    Henderson R. W., Goggans P. M., 2014, in AIP Conference Proceedings. pp 100--105, @doi 10.1063/1.4903717

    work page doi:10.1063/1.4903717 2014

  27. [27]

    Higson E., Handley W., Hobson M., Lasenby A., 2018, @doi [Bayesian Analysis] 10.1214/17-BA1075 , 13, 873

    work page doi:10.1214/17-ba1075 2018

  28. [28]

    Higson E., Handley W., Hobson M., Lasenby A., 2019, @doi [Statistics and Computing] 10.1007/s11222-018-9844-0 , 29, 891

    doi:10.1007/s11222-018-9844-0 2019

  29. [29]

    D., Sountsov P., 2022, in Camps-Valls G., Ruiz F

    Hoffman M. D., Sountsov P., 2022, in Camps-Valls G., Ruiz F. J. R., Valera I., eds, Proceedings of Machine Learning Research Vol. 151, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics. PMLR, pp 7799--7813, https://proceedings.mlr.press/v151/hoffman22a.html

    work page 2022

  30. [30]

    130, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics

    Hoffman M., Radul A., Sountsov P., 2021, in Banerjee A., Fukumizu K., eds, Proceedings of Machine Learning Research Vol. 130, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics. PMLR, pp 3907--3915, https://proceedings.mlr.press/v130/hoffman21a.html

    work page 2021

  31. [31]

    Hu Q., Veitch J., 2024, Costs of Bayesian Parameter Estimation in Third-Generation Gravitational Wave Detectors: a Review of Acceleration Methods ( @eprint arXiv 2412.02651 ), https://arxiv.org/abs/2412.02651

    work page arXiv 2024

  32. [32]

    Hu Z., Baryshnikov A., Handley W., 2024, @doi [Mon. Not. Roy. Astron. Soc.] 10.1093/mnras/stae1754 , 532, 4035

    doi:10.1093/mnras/stae1754 2024

  33. [33]

    pp 1--14

    Jouppi N., et al., 2023, in Proceedings of the 50th annual international symposium on computer architecture. pp 1--14

    work page 2023

  34. [34]

    Khan S., Husa S., Hannam M., Ohme F., P\"urrer M., Jim\'enez Forteza X., Boh\'e A., 2016, @doi [Phys. Rev. D] 10.1103/PhysRevD.93.044007 , 93, 044007

    doi:10.1103/physrevd.93.044007 2016

  35. [35]

    N., Williams N., Zimmerman A., 2023, Accelerated parameter estimation in Bilby with relative binning ( @eprint arXiv 2312.06009 ), https://arxiv.org/abs/2312.06009

    Krishna K., Vijaykumar A., Ganguly A., Talbot C., Biscoveanu S., George R. N., Williams N., Zimmerman A., 2023, Accelerated parameter estimation in Bilby with relative binning ( @eprint arXiv 2312.06009 ), https://arxiv.org/abs/2312.06009

    Pith/arXiv arXiv 2023

  36. [36]

    Leslie N., Dai L., Pratten G., 2021, @doi [Physical Review D] 10.1103/physrevd.104.123030 , 104

    doi:10.1103/physrevd.104.123030 2021

  37. [37]

    NVIDIA Corporation 2025, CUDA C++ Programming Guide , https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html

    work page 2025

  38. [38]

    M., 2003, @doi [The Annals of Statistics] 10.1214/aos/1056562461 , 31, 705

    Neal R. M., 2003, @doi [The Annals of Statistics] 10.1214/aos/1056562461 , 31, 705

    arXiv 2003

  39. [39]

    D., Houston M., Luebke D., Green S., Stone J

    Owens J. D., Houston M., Luebke D., Green S., Stone J. E., Phillips J. C., 2008, @doi [Proceedings of the IEEE] 10.1109/JPROC.2008.917757 , 96, 879

    arXiv 2008

  40. [40]

    Prathaban M., Handley W., 2024, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stae1908 , 533, 1839

    work page doi:10.1093/mnras/stae1908 2024

  41. [41]

    Prathaban M., et al., 2025b, blackjax\_ns\_gw: blackjax-ns for Gravitational Wave Inference on GPUs , https://github.com/mrosep/blackjax_ns_gw

    work page

  42. [42]

    Prathaban M., Yallup D., Alvey J., Yang M., Templeton W., Handley W., 2025a, Gravitational-wave inference at GPU speed: A bilby-like nested sampling kernel within blackjax-ns , @doi 10.5281/zenodo.17012011 , https://doi.org/10.5281/zenodo.17012011

    work page doi:10.5281/zenodo.17012011

  43. [43]

    Prathaban M., Bevins H., Handley W., 2025c, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staf962 , p. staf962

    doi:10.1093/mnras/staf962

  44. [44]

    Pratten G., et al., 2021, @doi [Phys. Rev. D] 10.1103/PhysRevD.103.104056 , 103, 104056

    doi:10.1103/physrevd.103.104056 2021

  45. [45]

    M., et al., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa2850 , 499, 3295

    Romero-Shaw I. M., et al., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa2850 , 499, 3295

    doi:10.1093/mnras/staa2850 2020

  46. [46]

    Skilling J., 2006, @doi [Bayesian Analysis] 10.1214/06-BA127 , 1, 833

    doi:10.1214/06-ba127 2006

  47. [47]

    Smith R. J. E., Ashton G., Vajpeyi A., Talbot C., 2020, @doi [Mon. Not. Roy. Astron. Soc.] 10.1093/mnras/staa2483 , 498, 4492

    doi:10.1093/mnras/staa2483 2020

  48. [48]

    S., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa278 , 493, 3132–3158

    Speagle J. S., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa278 , 493, 3132–3158

    doi:10.1093/mnras/staa278 2020

  49. [49]

    Global Optim.] 10.1023/A:1008202821328 , 11, 341

    Storn R., Price K., 1997, @doi [J. Global Optim.] 10.1023/A:1008202821328 , 11, 341

    doi:10.1023/a:1008202821328 1997

  50. [50]

    The LIGO Scientific Collaboration et al., 2015, @doi [Classical and Quantum Gravity] 10.1088/0264-9381/32/7/074001 , 32, 074001

    doi:10.1088/0264-9381/32/7/074001 2015

  51. [51]

    Thrane E., Talbot C., 2019, @doi [Publications of the Astronomical Society of Australia] 10.1017/pasa.2019.2 , 36

    doi:10.1017/pasa.2019.2 2019

  52. [52]

    Veitch J., et al., 2015, @doi [Physical Review D] 10.1103/physrevd.91.042003 , 91

    doi:10.1103/physrevd.91.042003 2015

  53. [53]

    J., Veitch J., Messenger C., 2021, @doi [Phys

    Williams M. J., Veitch J., Messenger C., 2021, @doi [Phys. Rev. D] 10.1103/PhysRevD.103.103006 , https://ui.adsabs.harvard.edu/abs/2021PhRvD.103j3006W 103, 103006

    doi:10.1103/physrevd.103.103006 2021

  54. [54]

    Wong K. W. K., Isi M., Edwards T. D. P., 2023a, Fast gravitational wave parameter estimation without compromises ( @eprint arXiv 2302.05333 ), https://arxiv.org/abs/2302.05333

    Pith/arXiv arXiv

  55. [55]

    Wong K. W. k., Gabri\'e M., Foreman-Mackey D., 2023b, @doi [J. Open Source Softw.] 10.21105/joss.05021 , 8, 5021

    doi:10.21105/joss.05021

  56. [56]

    Wouters T., Pang P. T. H., Dietrich T., Van Den Broeck C., 2024, @doi [Phys. Rev. D] 10.1103/PhysRevD.110.083033 , 110, 083033

    doi:10.1103/physrevd.110.083033 2024

  57. [57]

    Yallup D., Handley W., Cabezas J., et al., 2025b, blackjax : A Library of Bayesian Inference Algorithms in JAX (Nested Sampling Branch), https://github.com/handley-lab/blackjax/tree/nested_sampling

    work page

  58. [58]

    https://openreview.net/forum?id=ekbkMSuPo4

    Yallup D., Kroupa N., Handley W., 2025a, in Frontiers in Probabilistic Inference: Learning meets Sampling. https://openreview.net/forum?id=ekbkMSuPo4

    work page

  59. [59]

    Zackay B., Dai L., Venumadhav T., 2018, Relative Binning and Fast Likelihood Evaluation for Gravitational Wave Parameter Estimation ( @eprint arXiv 1806.08792 ), https://arxiv.org/abs/1806.08792

    Pith/arXiv arXiv 2018

  60. [60]

    ter Braak C. J. F., 2006, @doi [Statistics and Computing] 10.1007/s11222-006-8769-1 , 16, 239

    doi:10.1007/s11222-006-8769-1 2006

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.