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REVIEW 4 major objections 6 minor 61 references

RESOLVE: Rare Event Surrogate Likelihood for Gravitational Wave Paleontology Parameter Estimation

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read RESOLVE is the only surrogate model with correctly calibrated error bars on binary black hole formation efficiency, giving statistically valid credible intervals for the progenitor physics, including metallicity $0.0191^{+0.007}_{-0.076}$.

desk verdict Surrogate benchmark worth reading; headline credible intervals rest on a factor-of-10 conversion error and a rate-as-count Poisson likelihood. read the letter →

arxiv 2506.00757 v1 pith:UFYN74N3 submitted 2025-06-01 astro-ph.IM gr-qc

Ann-Kathrin Schuetz , Alexander Migala , Adam Boesky , Alan W.P. Poon , Floor S. Broekgaarden , Aobo Li This is my paper
classification astro-ph.IMgr-qc
keywords gravitational-wavepaleontologyrareeventsurrogatespolynomialchaosexpansionmulti-fidelityBayesianinferenceconditionalneuralprocessesbinaryblackholeformationefficiencyCOMPASpopulationsynthesiscredibleintervals
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tackles the central bottleneck of gravitational-wave paleontology: learning the physics of the massive-star progenitors of merging black holes when the forward simulator COMPAS produces so few mergers per run that the formation efficiency $\epsilon = m/N$ is a rare event, making cheap surrogates noisy and expensive ones unaffordable. RESOLVE claims to solve this with a multi-fidelity Bayesian polynomial chaos expansion (MF-BPCE) fed with continuous scores from a conditional neural process (CNP), which smooth the otherwise discrete collision outcomes; the resulting emulator is claimed to be the only surrogate among those benchmarked whose $1\sigma$, $2\sigma$, and $3\sigma$ posterior intervals cover out-of-sample high-fidelity COMPAS trials at the expected 68.27%, 95.45%, and 99.73% rates. The paper then converts the emulated efficiency into an expected merger rate with a constant factor, builds a Poisson likelihood against LIGO/Virgo's observed rate of $17^{+10}_{-6.7}\,\mathrm{yr^{-1}\,Gpc^{-3}}$, and runs MCMC to obtain credible intervals, tightly constraining metallicity to $0.0191^{+0.007}_{-0.076}$ while leaving $\alpha_{\mathrm{CE}}$, $\sigma_{\mathrm{BH}}$, and $\sigma_{\mathrm{NS}}$ broad. If the coverage claim survives, rare-event population-synthesis simulations can be turned into statistically valid posterior statements about stellar evolution rather than point estimates with hand-waved errors.

What carries the argument

The load-bearing object is the Multi-Fidelity Bayesian Polynomial Chaos Expansion (MF-BPCE), an autoregressive surrogate in which each fidelity level is a scalar-scaled copy of the level below plus a polynomial-chaos discrepancy term, $\hat{\epsilon}^{(f_i)}(\theta) = \rho^{(f_i)}\hat{\epsilon}^{(f_{i-1})}(\theta) + \sum_k c^{(f_i)}_k \Psi_k(\tilde{\theta})$, with $\Psi_k$ tensor products of Legendre polynomials and the coefficients, scalings, and noise variances treated as latent parameters inferred by Hamiltonian Monte Carlo. Feeding the lowest level is a Conditional Neural Process (CNP): it learns a Gaussian approximation to the latent collision probability $t(\theta,\phi)$ from the Bernoulli outcomes $X_{ji}$, and the per-trial average of its predicted means gives the smooth, denoised efficiency $\epsilon^{(f_0)}_{\mathrm{CNP}}$ that replaces the raw ratio $m/N$ as the cheap low-fidelity input. The expansion's job is to propagate epistemic uncertainty from the sparse high-fidelity trials and aleatoric noise from the low-fidelity trials into a posterior predictive $P(\hat{\epsilon}_* \mid \theta_*, D)$ whose calibration is then checked at $1\sigma$, $2\sigma$, and $3\sigma$; order selection uses cross-validated Lasso shrinkage, and the discrepancy polynomial order is fixed at 1 because only 5 to 15 high-fidelity trials are available.

What would settle it

Recompute the conversion of Appendix E, Eq. (9): with $s = 10^7\,M_\odot\,\mathrm{Gpc^{-3}\,yr^{-1}}$ and $\epsilon_r = 1.57133427\times10^{-6}/0.005$ events per solar mass, the product is $3142.66854$, not $314.266854$; a factor-of-ten error in $\hat{y}$ rescales the Poisson likelihood and would move every reported credible interval, including metallicity $0.0191^{+0.007}_{-0.076}$. Separately, the coverage claim can be settled directly: draw fresh out-of-sample high-fidelity COMPAS trials under the same training distribution and check whether the empirical $1\sigma/2\sigma/3\sigma$ coverage rates stay within sampling error of 68.27/95.45/99.73 percent, and check whether the recovered $\alpha_{\mathrm{CE}}$ trend persists when the 15 high-fidelity training points are resampled, since Appendix J shows that trend is visibly driven by those points.

Watch

Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that polynomial chaos beats Gaussian processes at emulating a rare formation efficiency when the low-fidelity input is denoised: across 150 out-of-sample high-fidelity COMPAS trials, the MF-BPCE posterior predictive places the true efficiency inside its $\pm 1\hat{\sigma}$, $\pm 2\hat{\sigma}$, and $\pm 3\hat{\sigma}$ bands 74%, 97%, and 100% of the time, matching the nominal 68.27%, 95.45%, and 99.73% coverage within sampling error, while the Gaussian-process-based RESuM model undercovers at $2\sigma$ and $3\sigma$ because it collapses to a near-flat trend in $\alpha_{\mathrm{CE}}$, $\sigma_{\mathrm{BH}}$, and $\sigma_{\mathrm{NS}}$, and the raw MFGP overcovers. Because the PCE coefficients are inferred by Hamiltonian Monte Carlo, the surrogate's posterior is carried forward into a Poisson likelihood $\ln L(\theta) = \sum_i \left(y_{\mathrm{obs},i}\ln\hat{y}_i(\theta) - \hat{y}_i(\theta) - \ln y_{\mathrm{obs},i}!\right)$ with $\hat{y} = 314.266854\,\hat{\epsilon}$, so that the MCMC posteriors over the four physics parameters are claimed to be community-standard credible intervals: metallicity $0.0191^{+0.007}_{-0.076}$, with the other three parameters unconstrained because their physical effects on merger efficiency are real but low-amplitude. The same pipeline also matches or beats the previous rare-event surrogate on a detector-design benchmark, which the paper offers as evidence that the method is not specific to COMPAS.

Load-bearing premise

The whole chain from simulated efficiency to observed rate rests on one constant conversion, $\hat{y} = 314.266854\,\hat{\epsilon}$, which the paper itself flags as oversimplified and whose stated value disagrees with its own Appendix E formula by a factor of ten ($1\times10^7 \times 1.57133427\times10^{-6}/0.005 = 3142.66854$); if that constant is wrong, the reported credible intervals shift or lose validity.

Editorial extensions

If this is right

  • If RESOLVE's calibration claim holds, astronomers can obtain statistically valid posterior intervals for binary black hole formation physics from as few as 5 to 15 high-fidelity COMPAS trials paired with roughly 1,000 cheap low-fidelity trials, without running $10^6$-system simulations at every posterior sample.
  • The metallicity constraint $Z = 0.0191^{+0.007}_{-0.076}$ derived from the 17 GWTC-3 events would stand as a community-standard measurement of the characteristic metallicity of merging binary black hole progenitors, directly comparable to independent population-synthesis analyses.
  • The benchmark results imply that the global-basis polynomial structure, not just the CNP denoising, is what recovers the subtle low-amplitude dependencies on $\alpha_{\mathrm{CE}}$, $\sigma_{\mathrm{BH}}$, and $\sigma_{\mathrm{NS}}$ that Gaussian-process surrogates flatten away.
  • The same likelihood construction, an emulated formation efficiency mapped to an expected rate and compared with observed counts through a Poisson term, extends to other observables such as double neutron star mergers once the rate conversion is upgraded beyond a single constant.

Reading between the lines

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

  • My inference: the coverage result is the paper's real product, and it is most fragile exactly where the paper concedes weakness, the constant rate conversion flagged in Section 6, whose stated value conflicts with Appendix E's own formula by a factor of ten, so a corrected conversion would rescale all the reported credible intervals.
  • My inference: the cleanest settlement of the scientific claim is to rerun the coverage test with new random seeds for the COMPAS initial conditions and with more than 15 high-fidelity trials, since Appendix J shows the $\alpha_{\mathrm{CE}}$ trend is visibly governed by those few points.
  • My inference: the same CNP-plus-PCE recipe should transfer to other rare binary outcomes such as double neutron star mergers and white dwarf collisions, and to any design problem whose metric is a small probability; the LEGEND benchmark already demonstrates that transfer in one such case.
  • My inference: using the surrogate's training posterior directly as the prior for the parameter-inference MCMC reuses the same simulation data in both stages, so the final credible intervals are best read as conditional on the surrogate rather than as fully hierarchical posterior statements.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper introduces RESOLVE, a multi-fidelity surrogate model that combines Conditional Neural Process preprocessing with a Bayesian Polynomial Chaos Expansion to emulate the rare binary-black-hole formation efficiency epsilon computed by COMPAS. The model is benchmarked against MFGP and RESuM on a LEGEND detector-design dataset and on new COMPAS data with 1000 low-fidelity and 15 high-fidelity training trials, with validation on 150 out-of-sample high-fidelity trials. The authors report MSE and 1/2/3-sigma coverage, claim that RESOLVE is the only surrogate achieving proper statistical coverage on the COMPAS benchmark, and then convert epsilon to a gravitational-wave rate using a constant factor. They combine the emulated rate with the LIGO/Virgo observed merger rate through a Poisson likelihood and report credible intervals for metallicity, alpha_CE, sigma_BH, and sigma_NS, with a central metallicity result of 0.0191^{+0.007}_{-0.076}.

Significance. If the surrogate coverage results are correct, the MF-BPCE architecture with CNP preprocessing is a useful and nontrivial contribution to rare-event surrogate modeling for binary population synthesis. The held-out COMPAS benchmark, the comparison against two prior surrogate models, and the detailed appendices are strengths; notably, the surrogate is evaluated on out-of-sample high-fidelity trials, so the benchmark is not circular in the sense that the LIGO rate is used only as data in the final likelihood. However, the likelihood construction contains concrete arithmetic and dimensional errors that invalidate the paper's central parameter-estimation deliverable as written. The credible intervals in Section 5 therefore cannot yet be regarded as community-standard results, and the claim that RESOLVE 'effectively learns the underlying distribution of each physics parameter' is not quantitatively supported.

major comments (4)
  1. [Section 3.2 and Appendix E, Eq. (9)] Equation (9) in Appendix E defines yhat = s * epsilon_r * epsilon with s = 1e7 M_sun Gpc^-3 yr^-1 and epsilon_r = 1.57133427e-6 / 0.005 events per M_sun. The product is 3142.66854, not 314.266854 as stated in Section 3.2 and used throughout the paper. This factor-of-10 discrepancy directly scales the surrogate output entering the likelihood, so the posterior credible intervals in Section 5, including the headline metallicity constraint, are not supported as written. The caveat in Section 6 that the conversion is 'oversimplified' does not repair the internal arithmetic error; please recompute the conversion factor and rerun the Bayesian inference.
  2. [Section 3.2, Eq. (5), and Section 5] The Poisson log-likelihood in Eq. (5) is dimensionally inconsistent. The observed quantity yobs is introduced in Section 5 as a rate, 17^{+10}_{-6.7} yr^-1 Gpc^-3, and yhat is also a rate, but Eq. (5) treats both as Poisson counts and includes factorial terms yobs_i!. A Poisson likelihood for rates requires an exposure factor, such as a survey volume times observing time or an integral over the detector horizon, to convert rates into expected counts. Section 5's statement that the inference is 'based on the 17 gravitational wave observations' further conflates the observed event count with the rate. Without a specified exposure, the likelihood and the resulting credible intervals are not well defined.
  3. [Section 4, Table 1, and Appendix I.1] The claim that RESOLVE is the only model with proper statistical coverage is weakened by model selection on the validation set. Section 4 states that the authors 'further examined different choices of polynomial order' and found that fourth-order polynomials yield optimal results, while Appendix I.1 describes K-fold cross-validation for order selection, but the coverage percentages in Table 1 are computed on the same 150 out-of-sample HF trials used to compare the other models. Post-selection coverage is optimistic. In addition, with only 150 validation trials, a 1-sigma coverage of 74% has a binomial standard error of about 3.8%, so the difference from the nominal 68.27% is not significant on its own; please report binomial confidence intervals for the coverage values and, ideally, select the polynomial order on a separate validation split or via nested cross-validation.
  4. [Section 4, Table 1, Figure 3, and Appendix J] The abstract's claim that RESOLVE 'effectively learns the underlying distribution of each physics parameter' is stronger than the evidence presented. Table 1 shows that RESOLVE has the highest MSE among all models on the black-hole dataset (e.g., 13.0e-6 versus 2.3e-6 for RESuM at 15 HF trials), and Appendix J concedes that the learned alpha_CE trend is driven by only 15 high-fidelity training points and may not generalize to the validation data. No quantitative metric is provided for the fidelity of the learned marginal parameter dependencies beyond visual inspection of Figure 3. I recommend either softening this claim or adding a quantitative validation of the learned trends, such as comparing predicted conditional means against binned high-fidelity validation data.
minor comments (6)
  1. [Introduction] LIGO did not announce the detection on September 14, 2015; the event GW150914 was observed on that date and the announcement was made on February 11, 2016. Please correct the wording.
  2. [Section 3.1] The phrase 'via it's posterior predictive' should be 'via its posterior predictive'; similar typographical issues appear elsewhere, such as 'aesaralibraries' in Appendix I and 'W AIC' in Section I.4.
  3. [Section 4 and Appendix C] The parameters sigma_BH and sigma_NS are described as 'the MSE of the Maxwellian distribution' from which kicks are sampled; these are scale parameters (standard deviations) of the kick distribution, and the term MSE is misleading.
  4. [Section 5] The sentence 'the likelihood functions is minimized' is grammatically incorrect and conceptually imprecise: in a Bayesian MCMC analysis one samples the posterior, and the likelihood itself is evaluated, not minimized.
  5. [Appendix F] Appendix F discusses quadrupole radiation from a rotating body, which is not the mechanism relevant to compact binary coalescence; this appendix appears disconnected from the rest of the paper and should be removed or rewritten to address binary inspiral radiation.
  6. [Appendix G] The phrase 'NP3-complex problem' appears to be a typo, likely for 'NP-hard' or 'NP-complete'; the attribution of optimal proposal spacing to Wiegand/Kish is also not standard MCMC theory, which relies on detailed balance and ergodicity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the surrogate benchmark is held-out and the likelihood uses LIGO data only as external input; the self-citations are not load-bearing.

full rationale

The derivation chain is not circular. The surrogate is trained on COMPAS low/high-fidelity trials, whose labels are the empirical efficiencies ϵRaw = m/N (Eq. 1), and it is evaluated on 150 out-of-sample high-fidelity trials (Section 4, Table 1). The observed LIGO/Virgo rate enters only at the likelihood stage (Section 5) and is not used to fit any surrogate parameter, so no fitted quantity is renamed as a prediction. The CNP preprocessing and the RESuM baseline are adopted from the authors' prior work, but the paper independently re-benchmarks MFGP, RESuM, and RESOLVE in Table 1, so the central coverage claim does not reduce to a self-citation. The Appendix E conversion and the constant in Section 3.2 are internally inconsistent (Eq. 9 yields 3142.67, not 314.266854, if evaluated as written), and the use of a rate in a Poisson count likelihood without an exposure factor is a units/correctness problem; neither is a definitional identity between input and output. The paper itself flags the conversion as 'oversimplified' and admits the αCE trend is driven by sparse HF training points (Section 6, Appendix J), which lowers reliability but is not circularity. Model-selection of the PCE order on the validation set is selection bias, not a fitted parameter called a prediction. No circular step meets the quote-and-reduction standard.

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

No new physical entities are introduced. The central claim rests on statistical modeling assumptions: independent Bernoulli outcomes, a known nuisance-parameter distribution, the Kennedy-O'Hagan autoregressive fidelity relationship, the validity of the CNP smoothing, and the constant conversion to a cosmic merger rate. The conversion factor is the most fragile, especially given the apparent arithmetic inconsistency.

free parameters (6)
  • PCE coefficients c_k^(fi) = not reported
    Latent coefficients of the polynomial chaos expansion at each fidelity level, inferred by Bayesian linear regression with zero-mean Gaussian priors.
  • Fidelity scaling rho^(fi) = not reported; prior mean set by minimizing MSE between LF and HF training data
    Scaling factor in the autoregressive multi-fidelity model, fit to training data.
  • Noise variance sigma^(fi) = HalfNormal(lambda) with lambda set to empirical std of HF data
    Noise level at each fidelity, calibrated to data.
  • Polynomial order d = 4 for BH dataset; LF order via cross-validation; HF discrepancy fixed to 1
    Model complexity selected by cross-validation and by validation-set coverage, a free choice that affects the reported results.
  • CNP network weights and hyperparameters = not specified
    Conditional neural process parameters trained on simulated events; architecture and hyperparameters are not given but affect the smoothed scores.
  • Conversion factor 314.266854 = 314.266854 (apparent inconsistency: should be 3142.66854 per Appendix E)
    Constant multiplier in the likelihood; the authors admit it is oversimplified, and its uncertainty is not propagated.
assumptions (6)
  • domain assumption Each COMPAS binary outcome X_i is an independent Bernoulli draw with probability t(theta, phi_i)
    Appendix A formalizes the simulation as independent Bernoulli trials; if COMPAS outcomes are correlated or the probability model is wrong, the formation efficiency variance is misstated.
  • domain assumption Nuisance parameters phi are sampled from a fixed joint distribution g(phi), stated as uniform
    The marginalized efficiency ebar(theta) in Eq. (7) assumes g(phi) is known and correct; the paper does not validate this against COMPAS defaults.
  • domain assumption Autoregressive linear multi-fidelity relation epsilon(fi) = rho^(fi) * epsilon(fi-1) + PCE discrepancy
    Kennedy-O'Hagan style assumption that higher fidelities are a scaled version of lower fidelities plus a smooth residual; not empirically validated on COMPAS data.
  • domain assumption CNP scores beta approximate the latent Bernoulli probability t(theta, phi)
    The method replaces discrete outcomes with smoothed CNP means; if the CNP is biased, the low-fidelity input to the PCE is biased.
  • domain assumption The local merger rate yobs is directly comparable to the simulated rate via a constant conversion, ignoring selection effects, time delays, and redshift evolution
    Section 3.2 and Appendix E establish this conversion; the authors explicitly list it as a limitation in Section 6.
  • domain assumption The selected four theta parameters and the default distributions of the other 23 parameters cover the relevant physics
    Section 4 and Appendix C fix the parameter space; if important physics is fixed or varied wrongly, the marginal credible intervals are misattributed.

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Cite this review

Pith. "Pith review of RESOLVE: Rare Event Surrogate Likelihood for Gravitational Wave Paleontology Parameter Estimation." pith.science (2026). https://pith.science/paper/UFYN74N3

@misc{pith2026250600757,
  author       = {Pith},
  title        = {Pith review of: RESOLVE: Rare Event Surrogate Likelihood for Gravitational Wave Paleontology Parameter Estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UFYN74N3}},
  note         = {Machine review of arXiv:2506.00757}
}
read the original abstract

The first detection of gravitational waves, recognized by the 2017 Nobel Prize in Physics, has opened up a new research field: gravitational-wave paleontology. When massive stars evolve into black holes and collide, they create gravitational waves that propagate through space and time. These gravitational-waves, now detectable on Earth, act as fossils tracing the histories of the massive stars that created them. Estimating physics parameters of these massive stars from detected gravitational-waves is a parameter estimation task, with the primary difficulty being the extreme rarity of collisions in simulated binary black holes. This rarity forces researchers to choose between prohibitively expensive simulations or accepting substantial statistical variance. In this work, we present RESOLVE, a rare event surrogate model that leverages polynomial chaos expansion (PCE) and Bayesian MCMC to emulate this rare formation efficiency. Our experimental results demonstrate that RESOLVE is the only surrogate model that achieves proper statistical coverage, while effectively learning the underlying distribution of each physics parameter. We construct a likelihood function incorporating both the emulated formation efficiency and LIGO's gravitational wave observations, which we then minimize to produce community-standard credible intervals for each physics parameter. These results enable astronomers to gain deeper insights into how the universe transformed from simple gases into the complex chemical environment that eventually made life possible.

Figures

Figures reproduced from arXiv: 2506.00757 by the authors.

Figure 1
Figure 1. Overview of the RESOLVE framework. The left side illustrates the CNP used for modeling [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Coverage plot of the RESOLVE model predictions on the binary black hole dataset (Trial [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Marginalized distribution of four θ parameters using different versions of formation efficiency ϵ as y axis: Row 1 (from top) uses ϵ LF Raw = m/N (light teal) and high-fidelity ϵ HF Raw = m/N (red) outputs, along with the averaged CNP score ϵ LF CNP (dark teal, see Eqn. 3); Row 2 is a zoomed-in version of ϵ LF CNP in Row 1; Row 3 uses the emulated ϵˆ from the RESOLVE model; Row 4 uses the emulated ϵˆ from the RESuM … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Posterior distributions and correlations of metallicity, [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Marginalized model predictions and data for the merger efficiency [PITH_FULL_IMAGE:figures/full_fig_p023_5.png]

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Reference graph

Works this paper leans on

61 extracted references · 27 canonical work pages

  1. [1]

    Aalbers et al

    J. Aalbers et al. Dark Matter Search Results from 4.2 Tonne-Years of Exposure of the LUX-ZEPLIN (LZ) Experiment . arXiv preprint arXiv:2410.17036, 10 2024

    arXiv 2024

  2. [2]

    B. P. Abbott et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett., 116: 0 061102, Feb 2016. doi:10.1103/PhysRevLett.116.061102. URL https://link.aps.org/doi/10.1103/PhysRevLett.116.061102

    doi:10.1103/physrevlett.116.061102 2016

  3. [3]

    Abbott , T

    R. Abbott , T. D. Abbott , F. Acernese , K. Ackley , C. Adams , N. Adhikari , R. X. Adhikari , V. B. Adya , C. Affeldt , D. Agarwal , M. Agathos , K. Agatsuma , N. Aggarwal , O. D. Aguiar , L. Aiello , A. Ain , P. Ajith , T. Akutsu , P. F. de Alarc \'o n , S. Akcay , S. Albanesi , A. Allocca , P. A. Altin , A. Amato , C. Anand , S. Anand , A. Ananyeva , S...

    2023

  4. [4]

    Abe et al

    S. Abe et al. Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen . Phys. Rev. Lett., 130 0 (5): 0 051801, 2023. doi:10.1103/PhysRevLett.130.051801

    doi:10.1103/physrevlett.130.051801 2023

  5. [5]

    Advanced Virgo : a second-generation interferometric gravitational wave detector

    F Acernese, M Agathos, K Agatsuma, D Aisa, N Allemandou, et al. Advanced Virgo : a second-generation interferometric gravitational wave detector. Classical and Quantum Gravity, 32 0 (2): 0 024001, December 2014. ISSN 1361-6382. doi:10.1088/0264-9381/32/2/024001. URL http://dx.doi.org/10.1088/0264-9381/32/2/024001. Publisher: IOP Publishing

    doi:10.1088/0264-9381/32/2/024001 2014

  6. [6]

    Agostini et al

    M. Agostini et al. Final Results of GERDA on the Search for Neutrinoless Double- Decay . Phys. Rev. Lett., 125 0 (25): 0 252502, 2020. doi:10.1103/PhysRevLett.125.252502

    doi:10.1103/physrevlett.125.252502 2020

  7. [7]

    Akutsu, M

    T. Akutsu, M. Ando, K. Arai, Y. Arai, S. Araki, et al. Kagra: 2.5 generation interferometric gravitational wave detector. Nature Astronomy, 3 0 (1): 0 35–40, January 2019. ISSN 2397-3366. doi:10.1038/s41550-018-0658-y. URL http://dx.doi.org/10.1038/s41550-018-0658-y

    doi:10.1038/s41550-018-0658-y 2019

  8. [8]

    Andrews , Simone S

    Jeff J. Andrews , Simone S. Bavera , Max Briel , Abhishek Chattaraj , Aaron Dotter , Tassos Fragos , Monica Gallegos-Garcia , Seth Gossage , Vicky Kalogera , Eirini Kasdagli , Aggelos Katsaggelos , Chase Kimball , Konstantinos Kovlakas , Matthias U. Kruckow , Camille Liotine , Devina Misra , Kyle A. Rocha , Dimitris Souropanis , Philipp M. Srivastava , Me...

    arXiv doi:10.48550/arxiv.2411.02376 2024

Show all 61 references
  1. [9]

    Aprile et al

    E. Aprile et al. First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment . Phys. Rev. Lett., 131 0 (4): 0 041003, 2023. doi:10.1103/PhysRevLett.131.041003

    2023 doi

  2. [10]

    I. J. Arnquist et al. Final Result of the Majorana Demonstrator s Search for Neutrinoless Double- Decay in Ge76 . Phys. Rev. Lett., 130 0 (6): 0 062501, 2023. doi:10.1103/PhysRevLett.130.062501

    2023 doi

  3. [11]

    Belczynski , J

    K. Belczynski , J. Klencki , C. E. Fields , A. Olejak , E. Berti , G. Meynet , C. L. Fryer , D. E. Holz , R. O'Shaughnessy , D. A. Brown , T. Bulik , S. C. Leung , K. Nomoto , P. Madau , R. Hirschi , E. Kaiser , S. Jones , S. Mondal , M. Chruslinska , P. Drozda , D. Gerosa , Z...

    2020

  4. [12]

    A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties

    Krzysztof Belczynski , Vassiliki Kalogera , and Tomasz Bulik . A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties . Astrophysics Journal, 572 0 (1): 0 407--431, June 2002. doi:10.1086/340304

    2002 doi

  5. [13]

    Rasio , Ronald E

    Krzysztof Belczynski , Vassiliki Kalogera , Frederic A. Rasio , Ronald E. Taam , Andreas Zezas , Tomasz Bulik , Thomas J. Maccarone , and Natalia Ivanova . Compact Object Modeling with the StarTrack Population Synthesis Code . APJS, 174 0 (1): 0 223--260, January 2008. doi:10....

    2008 doi

  6. [14]

    Boesky , Floor S

    Adam P. Boesky , Floor S. Broekgaarden , and Edo Berger . The Binary Black Hole Merger Rate Deviates from the Cosmic Star Formation Rate: A Tug of War between Metallicity and Delay Times . , 976 0 (1): 0 23, November 2024. doi:10.3847/1538-4357/ad7fe4

    2024 doi

  7. [15]

    Rodriguez , Kyle Kremer , Claire S

    Katelyn Breivik , Scott Coughlin , Michael Zevin , Carl L. Rodriguez , Kyle Kremer , Claire S. Ye , Jeff J. Andrews , Michael Kurkowski , Matthew C. Digman , Shane L. Larson , and Frederic A. Rasio . COSMIC Variance in Binary Population Synthesis . APJ, 898 0 (1): 0 71, July 2...

    2020 doi

  8. [16]

    stroopwafel: simulating rare outcomes from astrophysical populations, with application to gravitational-wave sources

    Floor S Broekgaarden, Stephen Justham, Selma E de Mink, Jonathan Gair, Ilya Mandel, Simon Stevenson, Jim W Barrett, Alejandro Vigna-Gómez, and Coenraad J Neijssel. stroopwafel: simulating rare outcomes from astrophysical populations, with application to gravitational-wave sour...

    2019 doi

  9. [17]

    Broekgaarden , Edo Berger , Simon Stevenson , Stephen Justham , Ilya Mandel , Martyna Chru \'s li \'n ska , Lieke A

    Floor S. Broekgaarden , Edo Berger , Simon Stevenson , Stephen Justham , Ilya Mandel , Martyna Chru \'s li \'n ska , Lieke A. C. van Son , Tom Wagg , Alejandro Vigna-G \'o mez , Selma E. de Mink , Debatri Chattopadhyay , and Coenraad J. Neijssel . Impact of massive binary star...

    2022 doi

  10. [18]

    Christian G. Bucher. Adaptive sampling—an iterative fast monte carlo procedure. Structural Safety, 5 0 (2): 0 119--126, 1988

    1988

  11. [19]

    The DNNLikelihood : enhancing likelihood distribution with Deep Learning

    Andrea Coccaro, Maurizio Pierini, Luca Silvestrini, and Riccardo Torre. The DNNLikelihood : enhancing likelihood distribution with Deep Learning . The European Physical Journal C, 80 0 (7): 0 664, July 2020. ISSN 1434-6052. doi:10.1140/epjc/s10052-020-8230-1. URL https://doi.o...

    2020 doi

  12. [20]

    Planck 2018 results

    Planck Collaboration, N Aghanim, Y Akrami, M Ashdown, J Aumont, C Baccigalupi, M Ballardini, AJ Banday, RB Barreiro, N Bartolo, et al. Planck 2018 results. vi. cosmological parameters. Astronomy & Astrophysics, 641: 0 A6, 2020

    2018

  13. [21]

    Observation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc

    The ATLAS Collaboration. Observation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc. Physics Letters B, 716 0 (1): 0 1--29, 2012. ISSN 0370-2693. doi:https://doi.org/10.1016/j.physletb.2012.08.020. URL https://www.scienced...

    2012 doi

  14. [22]

    Lectures on statistics in theory: Prelude to statistics in practice

    Robert D Cousins. Lectures on statistics in theory: Prelude to statistics in practice. arXiv preprint arXiv:1807.05996, 2018

    2018 arXiv

  15. [23]

    Asymptotic formulae for likelihood-based tests of new physics

    Glen Cowan, Kyle Cranmer, Eilam Gross, and Ofer Vitells. Asymptotic formulae for likelihood-based tests of new physics. The European Physical Journal C, 71 0 (2): 0 1--19, 2011

    2011

  16. [24]

    Physics-informed neural networks as surrogate models of hydrodynamic simulators

    James Donnelly, Alireza Daneshkhah, and Soroush Abolfathi. Physics-informed neural networks as surrogate models of hydrodynamic simulators. Science of The Total Environment, 912: 0 168814, 2024. ISSN 0048-9697. doi:https://doi.org/10.1016/j.scitotenv.2023.168814. URL https://w...

    2024

  17. [25]

    a herungsweise integration der feldgleichungen der gravitation. Sitzungsberichte der K \

    Albert Einstein. N \"a herungsweise integration der feldgleichungen der gravitation. Sitzungsberichte der K \"o niglich Preu ischen Akademie der Wissenschaften , pages 688--696, 1916

    1916

  18. [26]

    U ber gravitationswellen. Sitzungsberichte der K \

    Albert Einstein. \"U ber gravitationswellen. Sitzungsberichte der K \"o niglich Preu ischen Akademie der Wissenschaften , pages 154--167, 1918

    1918

  19. [27]

    Unified approach to the classical statistical analysis of small signals

    Gary J Feldman and Robert D Cousins. Unified approach to the classical statistical analysis of small signals. Physical Review D, 57 0 (7): 0 3873, 1998

    1998

  20. [28]

    Multinest: an efficient and robust bayesian inference tool for cosmology and particle physics

    Farhan Feroz, Michael P Hobson, and Mike Bridges. Multinest: an efficient and robust bayesian inference tool for cosmology and particle physics. Monthly Notices of the Royal Astronomical Society, 398 0 (4): 0 1601--1614, 2009

    2009

  21. [29]

    Andrews , Simone S

    Tassos Fragos , Jeff J. Andrews , Simone S. Bavera , Christopher P. L. Berry , Scott Coughlin , Aaron Dotter , Prabin Giri , Vicky Kalogera , Aggelos Katsaggelos , Konstantinos Kovlakas , Shamal Lalvani , Devina Misra , Philipp M. Srivastava , Ying Qin , Kyle A. Rocha , Jaime ...

    2023

  22. [30]

    Maddison, Tiago Ramalho, David Saxton, Murray Shanahan, Yee Whye Teh, Danilo J

    Marta Garnelo, Dan Rosenbaum, Chris J. Maddison, Tiago Ramalho, David Saxton, Murray Shanahan, Yee Whye Teh, Danilo J. Rezende, and S. M. Ali Eslami. Conditional neural processes, 2018. URL https://arxiv.org/abs/1807.01613

    2018 arXiv

  23. [31]

    The progenitors of compact-object binaries: impact of metallicity, common envelope and natal kicks

    Nicola Giacobbo and Michela Mapelli . The progenitors of compact-object binaries: impact of metallicity, common envelope and natal kicks . MNRAS, 480 0 (2): 0 2011--2030, October 2018. doi:10.1093/mnras/sty1999

    2011 doi

  24. [32]

    Merging black hole binaries: the effects of progenitor's metallicity, mass-loss rate and Eddington factor

    Nicola Giacobbo , Michela Mapelli , and Mario Spera . Merging black hole binaries: the effects of progenitor's metallicity, mass-loss rate and Eddington factor . MNRAS, 474 0 (3): 0 2959--2974, March 2018. doi:10.1093/mnras/stx2933

    2018 doi

  25. [33]

    Hurley , Onno R

    Jarrod R. Hurley , Onno R. Pols , and Christopher A. Tout . Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity . MNRAS, 315 0 (3): 0 543--569, July 2000. doi:10.1046/j.1365-8711.2000.03426.x

  26. [34]

    Probability

    John Pitman . Probability. Springer-Verlag New York, Inc., New York, 1993. ISBN 978-0-387-94594-1

    1993

  27. [35]

    M. C. Kennedy and A. O’Hagan. Predicting the output from a complex computer code when fast approximations are available. Biometrika, vol. 87 0 (no. 1): 0 1–13, 2000

    2000

  28. [36]

    Evaluation of failure probability via surrogate models

    Jing Li and Dongbin Xiu. Evaluation of failure probability via surrogate models. Journal of Computational Physics, 229 0 (23): 0 8966--8980, 2010

    2010

  29. [37]

    An efficient surrogate-based method for computing rare failure probability

    Jing Li, Jinglai Li, and Dongbin Xiu. An efficient surrogate-based method for computing rare failure probability. Journal of Computational Physics, 230 0 (24): 0 8683--8697, 2011

    2011

  30. [38]

    Cosmic Star Formation History

    Piero Madau and Mark Dickinson. Cosmic Star Formation History . Ann. Rev. Astron. Astrophys., 52: 0 415--486, 2014. doi:10.1146/annurev-astro-081811-125615

    2014 doi

  31. [39]

    Rosenbluth, Marshall N

    Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. Equation of State Calculations by Fast Computing Machines . The Journal of Chemical Physics, 21 0 (6): 0 1087--1092, June 1953. ISSN 0021-9606. doi:10.1063/1.1699114. URL ...

    1953 doi

  32. [40]

    Geometry aware physics informed neural network surrogate for solving Navier – Stokes equation ( GAPINN )

    Jan Oldenburg, Finja Borowski, Alper Öner, Klaus-Peter Schmitz, and Michael Stiehm. Geometry aware physics informed neural network surrogate for solving Navier – Stokes equation ( GAPINN ). Advanced Modeling and Simulation in Engineering Sciences, 9 0 (1): 0 8, June 2022. ISSN...

    2022 doi

  33. [41]

    Sequential importance sampling for structural reliability analysis

    Iason Papaioannou, Costas Papadimitriou, and Daniel Straub. Sequential importance sampling for structural reliability analysis. Structural Safety, 62: 0 66--75, 2016

    2016

  34. [42]

    Multifidelity importance sampling

    Benjamin Peherstorfer, Tiangang Cui, Youssef Marzouk, and Karen Willcox. Multifidelity importance sampling. Computer Methods in Applied Mechanics and Engineering, 300: 0 490--509, 2016

    2016

  35. [43]

    Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation

    Benjamin Peherstorfer, Boris Kramer, and Karen Willcox. Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation. SIAM/ASA Journal on Uncertainty Quantification, 6 0 (2): 0 737--761, 2018

    2018

  36. [44]

    P. C. Peters. Gravitational radiation and the motion of two point masses. Phys. Rev., 136: 0 B1224--B1232, Nov 1964. doi:10.1103/PhysRev.136.B1224. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1224

    1964 doi

  37. [45]

    Pols, Klaus-Peter Schröder, Jarrod R

    Onno R. Pols, Klaus-Peter Schröder, Jarrod R. Hurley, Christopher A. Tout, and Peter P. Eggleton. Stellar evolution models for z = 0.0001 to 0.03. Monthly Notices of the Royal Astronomical Society, 298 0 (2): 0 525--536, 1998. doi:10.1046/j.1365-8711.1998.01658.x

    1998

  38. [46]

    , Poojan Agrawal , Jim W

    Riley, J. , Poojan Agrawal , Jim W. Barrett , Kristan N. K. Boyett , Floor S. Broekgaarden , Debatri Chattopadhyay , Sebastian M. Gaebel , Fabian Gittins , Ryosuke Hirai , George Howitt , Stephen Justham , Lokesh Khandelwal , Floris Kummer , Mike Y. M. Lau , Ilya Mandel , Selm...

    2022

  39. [47]

    Santosh Kumar Sasanapuri, C. T. Dhanya, and A. K. Gosain. A surrogate machine learning model using random forests for real-time flood inundation simulations. Environmental Modelling & Software, 188: 0 106439, 2025. ISSN 1364-8152. doi:https://doi.org/10.1016/j.envsoft.2025.106...

    2025

  40. [48]

    Poon, and Aobo Li

    Ann-Kathrin Schuetz, A.W.P. Poon, and Aobo Li. RES um: A rare event surrogate model for physics detector design. In The Thirteenth International Conference on Learning Representations, 2025. URL https://openreview.net/forum?id=lqTILjL6lP

    2025

  41. [49]

    A Novel Convolutional - Autoencoder Based Surrogate Model for Fast S -parameter Calculation of Planar BPFs

    Ren Shibata, Masataka Ohira, and Zhewang Ma. A Novel Convolutional - Autoencoder Based Surrogate Model for Fast S -parameter Calculation of Planar BPFs . In 2022 IEEE / MTT - S International Microwave Symposium - IMS 2022 , pages 498--501, 2022. doi:10.1109/IMS37962.2022.9865285

    2022

  42. [50]

    Joshua S. Speagle. A conceptual introduction to markov chain monte carlo methods, 2020. URL https://arxiv.org/abs/1909.12313

    2020 arXiv

  43. [51]

    Gravitation and Cosmology

    Steven Weinberg . Gravitation and Cosmology . John Wiley & Sons, Inc., 1972. ISBN 0-417-92567-5

    1972

  44. [52]

    Barrett, Coenraad J

    Simon Stevenson, Alejandro Vigna-Gómez, Ilya Mandel, Jim W. Barrett, Coenraad J. Neijssel, David Perkins, and Selma E. de Mink. Formation of the first three gravitational-wave observations through isolated binary evolution. Nature Communications, 8: 0 14906, April 2017. doi:10...

    2017 arXiv

  45. [53]

    Inverse decision-making using neural amortized bayesian actors

    Dominik Straub, Tobias F Niehues, Jan Peters, and Constantin A Rothkopf. Inverse decision-making using neural amortized bayesian actors. arXiv preprint arXiv:2409.03710, 2024

    2024 arXiv

  46. [54]

    Bayes in the sky: Bayesian inference and model selection in cosmology

    Roberto Trotta. Bayes in the sky: Bayesian inference and model selection in cosmology. Contemporary Physics, 49 0 (2): 0 71--104, 2008

    2008

  47. [55]

    Neijssel, Simon Stevenson, Jim W

    Alejandro Vigna-Gómez, Coenraad J. Neijssel, Simon Stevenson, Jim W. Barrett, Krzysztof Belczynski, Stephen Justham, Selma E. de Mink, Bernhard Müller, Philipp Podsiadlowski, Mathieu Renzo, Dorottya Szécsi, and Ilya Mandel. On the formation history of Galactic double neutron s...

    2018 arXiv

  48. [56]

    Multilevel sequential importance sampling for rare event estimation

    Felix Wagner, Jonas Latz, Iason Papaioannou, and Elisabeth Ullmann. Multilevel sequential importance sampling for rare event estimation. SIAM Journal on Scientific Computing, 42 0 (4): 0 A2062--A2087, 2020

    2020

  49. [57]

    The ensemble kalman filter for rare event estimation

    Felix Wagner, Iason Papaioannou, and Elisabeth Ullmann. The ensemble kalman filter for rare event estimation. SIAM/ASA Journal on Uncertainty Quantification, 10 0 (1): 0 317--349, 2022

    2022

  50. [58]

    H. Wiegand. Kish, L .: Survey Sampling . John Wiley & Sons , Inc ., New York , London 1965, IX + 643 S ., 31 Abb ., 56 Tab ., Preis 83 s. Biometrische Zeitschrift, 10 0 (1): 0 88--89, 1968. doi:https://doi.org/10.1002/bimj.19680100122. URL https://onlinelibrary.wiley.com/doi/a...

    1965 doi

  51. [59]

    Physics-informed neural networks for data-free surrogate modelling and engineering optimization – An example from composite manufacturing

    Tobias Würth, Constantin Krauß, Clemens Zimmerling, and Luise Kärger. Physics-informed neural networks for data-free surrogate modelling and engineering optimization – An example from composite manufacturing. Materials & Design, 231: 0 112034, 2023. ISSN 0264-1275. doi:https:/...

    2023

  52. [60]

    The wiener--askey polynomial chaos for stochastic differential equations

    Dongbin Xiu and George Em Karniadakis. The wiener--askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing, 24 0 (2): 0 619--644, 2002

    2002

  53. [61]

    Z. Fu , Ch. Grant , D. M. Krawiec , A. Li , and L. A. Winslow . Generative models for simulation of kamland-zen. The European Physical Journal C, 84 0 (6): 0 651, 2024

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.