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Efficient Bayesian Sampling with Langevin Birth-Death Dynamics

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read An ensemble Langevin sampler augmented with birth-death dynamics recovers the GW150914 posterior modes in about 15 minutes on a GPU, though it systematically overconstrains the parameters.

desk verdict A promising GW mode finder with a real stationarity problem: the kernel-smoothed birth-death rate in Eq. (12) is not zero at ρ=p, so the target is not the stationary distribution, and the paper's own overconstraint observation is the expected signature. read the letter →

arxiv 2509.01942 v1 pith:WIZPZPVB submitted 2025-09-02 stat.AP gr-qc

Alex Leviyev , Francesco Iacovelli , Aaron Zimmerman This is my paper
classification stat.APgr-qc MSC 62F1565C05 PACS 02.50.Tt04.30.-w
keywords Langevindynamicsbirth-deathprocessBayesianinferenceensemblesamplingFisherpreconditioninggravitationalwaveparameterestimationGW150914non-Euclidean
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 proposes a first-order, GPU-parallel sampling method for Bayesian posterior estimation by combining Langevin diffusion with a birth-death process. The method rescales the dynamics with an ensemble Fisher preconditioner, defines a principled way to push the flow onto hypercube and hypertorus domains, and adds annealing to help particles escape shallow modes. On toy problems, the combination finds and weight-balances modes that ordinary Langevin dynamics misses, converging several times faster than the unpreconditioned flow. The paper then shows the method recovers the parameters of GW150914, the first detected binary black hole merger, in about 15 minutes on a GPU, where a nested-sampling reference took roughly 1.5 hours on many CPUs. The authors note the recovered posterior is systematically overconstrained, so the demonstrated strength is fast mode recovery rather than unbiased credible intervals.

What carries the argument

The machinery is an ensemble Langevin diffusion whose drift and noise are preconditioned by the inverse of the ensemble Fisher covariance matrix (Eq. 7), combined with a birth-death jump process (Algorithm 1) with rate Λ(x;ρ)=ln((k∗ρ)/p)(x)−E_ρ[ln((k∗ρ)/p)], where k is a Gaussian kernel with bandwidth set by the median heuristic. Reparameterization Theorem 2.3 transfers the dynamics from R^d to a hypercube or hypertorus by composing an affine map with the quantile function of a continuous random variable, adding the log-density of that variable as a confining potential. The Fisher preconditioner accelerates convergence on ill-conditioned targets, the birth-death rate pushes particles out of

What would settle it

On a known multimodal target, run the full birth-death sampler with several kernel bandwidths and compare recovered mixture weights and the energy two-sample statistic against exact i.i.d. draws; if the discrepancy persists across all bandwidths and annealing schedules, the stationary distribution differs from p.

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Extended reading notes

Core claim

Using an ensemble of 500 particles and 20,000 iterations with Fisher preconditioning, a linear annealing schedule, and the kernel-smoothed birth-death rate, the method reproduces the main modes of the GW150914 posterior, matching a nested-sampling reference computed with a marginalized likelihood. The execution time is about 15 minutes on a GPU, with model and gradient evaluations embarrassingly parallel; the reference took about 1.5 hours on a CPU cluster. The authors state that the dynamics recovers the modes of the posterior well but systematically overconstrains the parameters, and attribute this to the absence of Metropolis-Hastings corrections in the diffusion and to sensitivity of the

Load-bearing premise

The sampler's unbiasedness depends on the kernel-smoothed birth-death rate being identically zero at the target and on the unadjusted Langevin step being a faithful discretization; the rate is not exactly zero for a Gaussian kernel, and the discretization has no Metropolis correction, so the stationary target is only approximate.

Editorial extensions

If this is right

  • If the approach holds up, gravitational-wave parameter estimation can move from hours on large CPU clusters to tens of minutes on a single GPU for aligned-spin models.
  • The reparameterization theorem provides a general recipe for Langevin-type samplers on constrained and periodic domains, with the Gaussian choice acting as an L2-style confining potential.
  • Birth-death augmentation plus annealing recovers multimodal weights in test cases where plain Langevin dynamics remains trapped, suggesting wider use for multimodal posteriors.
  • Because the method is only first-order and parallelizes over particles, it is a natural fit for algorithmic differentiation and hardware accelerators.
  • The reported systematic overconstraint implies the current sampler is a fast mode-finder, not yet an unbiased posterior sampler, and needs a Metropolis filter or exact jump rule for credible intervals.

Reading between the lines

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

  • The overconstraint is consistent with the stationary distribution of the birth-death process differing from p when the kernel rate Λ does not vanish at ρ=p; this should be checked by tuning the kernel bandwidth on a known target.
  • The same dynamics should transfer to other differentiable waveform models and to neutron-star parameter estimation, because only the log-likelihood gradient and product-space structure are needed.
  • A stepwise ablation—switching off birth-death, then adding an exact jump scheme—would quantitatively separate the contribution of the unadjusted Langevin bias from that of the kernel-smoothed rate.
  • The quantile-map framework suggests designing custom reparameterizations that adapt the confining potential to prior shapes with boundary mass, going beyond the Gaussian, logistic, and Cauchy examples.
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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

3 major / 4 minor

Summary. The paper introduces an ensemble Langevin sampler augmented with a birth-death process, together with ensemble-based Fisher preconditioning, reparameterizations for hypercube/torus supports, and an annealing schedule. The method is first-order and parallelized across particles, and it is demonstrated on toy problems and on the GW150914 parameter-estimation problem. The authors report that the sampler recovers the modes of the GW150914 posterior in about 15 minutes on a GPU, compared with about 1.5 hours for a nested-sampling run, but they also acknowledge in Section 4 that the recovered distribution 'systematically overconstrains the parameters.'

Significance. If the stationarity issue identified below is repaired, the paper would be a useful contribution: it combines several practical ingredients (ensemble preconditioning, reparameterization, birth-death jumps, topological support) into a GPU-friendly first-order sampler, and the reparameterization analysis in Theorem 2.3 and Appendix B is mathematically clean. The code is available, and the experiments are reproducible in principle. However, the paper's central claim of 'recovering the posterior' is not supported by the current algorithm because the birth-death rate used in the implementation does not leave the target invariant.

major comments (3)
  1. [Eq. (12) and Section 2.4] The paper states that the kernel-smoothed rate Λ(x;ρ)=ln((k*ρ)/p)(x) - E_{x'∼ρ}[ln((k*ρ)/p)(x')] is 'identically zero when ρ=p'. This is false for any non-delta kernel. For the Gaussian kernel of Eq. (13), take p=N(0,1) and k=N(0,h²); then k*p=N(0,1+h²), so ln((k*p)/p)(x)=const + [h²/(2(1+h²))]x², and centering gives Λ(x;p)=[h²/(2(1+h²))](x²-1), which is not zero. Consequently p is not a stationary point of the birth-death term used in Algorithm 1. The mean-field equilibrium of the pure birth-death dynamics instead satisfies k*ρ∝p, whose Gaussian solution has variance σ_p²-h², i.e. a narrower distribution. This provides a concrete mechanism for the 'systematically overconstrains' behavior reported in Section 4, and it cannot be removed by adding a Metropolis filter to the diffusion alone. The unsmoothed rate in Eq. (11) does have the claimed property, but the implemented smoothed rate do
  2. [Section 4 and Abstract] The abstract claims the method is 'successfully applied to recover the parameters of GW150914', but Section 4 states that the dynamics 'recovers the modes of the posterior well, but systematically overconstrains the parameters.' These statements are in tension. The supported claim is fast mode discovery, not posterior recovery. The comparison with parallel Bilby is also not apples-to-apples: the Bilby run uses a likelihood marginalized over dL, tc, and Φc, whereas the Langevin birth-death run uses the full likelihood over all parameters, so the two runs target different posterior distributions. The reported speedup should be qualified accordingly, or the comparison should be rerun on identical targets.
  3. [Section 3.4 / Fig. 4] The two-ring Gaussian mixture experiment is presented as evidence that birth-death 'balances' mode weights. However, if the stationarity error from Eq. (12) is present, the balance achieved may be a balance with respect to the biased equilibrium k*ρ∝p rather than the true posterior. The experiment should be repeated with a corrected rate or with a diagnostic that isolates the birth-death bias (e.g. running the pure birth-death dynamics without diffusion and comparing the stationary variance to p). Without this, the mode-weight recovery claim is not established.
minor comments (4)
  1. [Eq. (12) / Remark 2.4] Remark 2.4 lists desirable properties of the unsmoothed rate, but the smoothing in Eq. (12) is stated to break diffeomorphic invariance. It would help to also state explicitly that smoothing breaks the exact stationarity property, since this is not merely a technicality.
  2. [Section 4, hyperparameters] The hyperparameters γ=0.01ϵ, σ=0.01 appear without definition of ϵ and σ in the main text; later τ and f are defined. Please define all tunables in one place and clarify the relationship between γ, τ, and the jump rate.
  3. [Throughout] There are several typographical errors (e.g. 'embarassingly', 'reparamaterization', 'Guassian', 'correponding', 'retrainment'). These do not affect the science but should be corrected.
  4. [Fig. 5 caption] The caption says the results are 'in reasonable agreement', while the text says the parameters are systematically overconstrained. Please make the caption consistent with the quantitative assessment, and report numerical discrepancy measures (e.g. marginal means/credible intervals) rather than relying only on the corner plot.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: adaptive ensemble preconditioning and kernel rates are self-referential only in the standard sense; the GW benchmark is external and the supported claim is fast mode recovery with acknowledged bias.

full rationale

Score 0: no step in the paper reduces by construction to its inputs. The Langevin update (Eq. 3) and preconditioned update (Eq. 4) are standard; the Fisher preconditioner (Eq. 7) is a Monte-Carlo estimator of the target-gradient covariance (Eq. 6), and using the evolving ensemble for that estimate is adaptive preconditioning, not a fitted parameter renamed as a prediction. The reparameterization theorem (Theorem 2.3, Eqs. 8-9) is proved in-text by a change of variables, and its three variants (logistic/Gaussian/Cauchy) are compared rather than assumed. The birth-death rate (Eq. 12) adapts the external construction of [37,46]; no uniqueness or optimality claim from the present authors' prior work is used to force the choice of kernel, which is explicitly a modeling choice (Eq. 13). The GW150914 validation is against an independent Dynesty/Bilby run using the same data, waveform, and priors, with no posterior summary from Bilby fed into the sampler; the paper's own Section 4 states the dynamics 'recover the modes ... but systematically overconstrain the parameters,' so the supported claim is mode recovery, and the acknowledged bias is a correctness limitation, not a circularity. The only in-scope caveat is the assertion in Section 2.4 that the smoothed rate Lambda in Eq. (12) is 'identically zero when rho = p'; for the Gaussian kernel of Eq. (13), k*p != p, so this stationarity claim is false and the birth-death term has an intrinsic bias. This is a mathematical error that should be weighed in correctness, but it does not make any predicted output equivalent to an input. The self-citations [27,31,32] refer to software and code repositories, not to load-bearing theoretical results.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The math core uses standard change-of-variables and diffusion results; the load-bearing approximations are the kernel-smoothed birth-death rate, the decoupled jump scheme, and the unadjusted (biased) Langevin update. The claimed stationarity of Eq. (12) is false for a Gaussian kernel, which is the main structural weakness.

free parameters (5)
  • Fisher damping lambda = 0.001
    Added to the ensemble Fisher matrix in Eq. (7) for numerical stability; used in toy experiments and implicitly in GW run.
  • Langevin timestep tau = 0.001 (identity), 2 (Fisher) in toy; 0.5 in GW150914
    Hand-chosen for stability and speed; the preconditioning comparison in Fig. 2 uses different timesteps per method, which complicates the comparison.
  • Annealing schedule beta_min = 10^-5, linear to 1
    Sets how much the posterior is heated for exploration; chosen without sensitivity study.
  • Maximum teleportation fraction f = 0.05 in GW run
    Controls jump rarity and hence the validity of the decoupled jump approximation; adaptive scaling c is tuned to meet it.
  • Kernel bandwidth h = median heuristic of pairwise distances
    Birth-death rate uses kernel density estimates; the paper claims insensitivity on the two-ring problem but kernel choice is a known source of bias.
assumptions (6)
  • standard math Langevin diffusion converges to the Gibbs density e^{-V} under the Fokker-Planck equation
    Section 2.1, Eq. (2), citing [48]. This is the basis for setting V = -ln p.
  • standard math Pushforward density formula: p#(y) = p(T^{-1}(y)) |det grad T^{-1}(y)|
    Used directly in the proof of Theorem 2.3, Section 2.3.
  • domain assumption Continuous birth-death PDE (Eq. 10) converges to p with potential-independent rate, as shown in [37]
    Imported in Section 2.4, Remark 2.4, and used to argue robustness to conditioning and multimodality.
  • ad hoc to paper The kernel-smoothed rate Lambda in Eq. (12) with Gaussian kernel (Eq. 13) preserves the stationary distribution p
    No proof is given; for a Gaussian kernel, Lambda(x;p) is not identically zero unless k*p=p, so the target p is not stationary under the smoothed birth-death process.
  • domain assumption ULA without Metropolis correction has negligible bias for these targets at chosen timestep
    Section 4, 'we do not incorporate Metropolis-Hastings corrections in the diffusion, and this naturally makes the diffusion biased [62]'; the paper observes the resulting systematic overconstraint.
  • domain assumption Cylindrical approximation of S^2 with pole distortion is acceptable for orientation parameters
    Section 2.7, 'this simplicity comes at the cost of significant distortions near the poles'.

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Cite this review

Pith. "Pith review of Efficient Bayesian Sampling with Langevin Birth-Death Dynamics." pith.science (2026). https://pith.science/paper/WIZPZPVB

@misc{pith2026250901942,
  author       = {Pith},
  title        = {Pith review of: Efficient Bayesian Sampling with Langevin Birth-Death Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WIZPZPVB}},
  note         = {Machine review of arXiv:2509.01942}
}
read the original abstract

Bayesian inference plays a central role in scientific and engineering applications by enabling principled reasoning under uncertainty. However, sampling from generic probability distributions remains a computationally demanding task. This difficulty is compounded when the distributions are ill-conditioned, multi-modal, or supported on topologically non-Euclidean spaces. Motivated by challenges in gravitational wave parameter estimation, we propose simulating a Langevin diffusion augmented with a birth-death process. The dynamics are rescaled with a simple preconditioner, and generalized to apply to the product spaces of a hypercube and hypertorus. Our method is first-order and embarrassingly parallel with respect to model evaluations, making it well-suited for algorithmic differentiation and modern hardware accelerators. We validate the algorithm on a suite of toy problems and successfully apply it to recover the parameters of GW150914 -- the first observed binary black hole merger. This approach addresses key limitations of traditional sampling methods, and introduces a template that can be used to design robust samplers in the future.

Figures

Figures reproduced from arXiv: 2509.01942 by the authors.

Figure 1
Figure 1. Diagram showing the composition of maps defining [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Convergence of Langevin dynamics with (left panel) optimal Fisher preconditioning and (right panel) differ￾ent random variables for reparameterization. We plot the evolution of the energy 2-sample statistic [47, 57] between the evolving ensemble and i.i.d samples from the target. (left panel) We see that the flow with Fisher preconditioning converges quickly, while the flow without preconditioning requires many more… view at source ↗
Figure 3
Figure 3. Final samples produced by the Langevin dynamics in its standard implementation ( [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Convergence with respect to the ϵ-statistic [47, 57]. (left panel) shows a comparison between the sampling methods. (right panel) shows the sensitivity to bandwidth h. bandwidth in Eq. (13). This is likely due to an imbalance between the energy and distance terms in th…
Figure 5
Figure 5. Figure 5: A corner-plot comparing samples obtained from the birth-death process (blue) and samples obtained from [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Illustration of how the kill method works. An ensemble of size N = 5 is initialized, and the output of two consectutive kill operations are recorded. Dead particles are shaded in light grey. −15 −10 −5 5 10 15 2 4 6 U(y) −6 −4 −2 2 4 6 0.5 1 1.5 d 2U(y) dy2 Cauchy Gaus…
Figure 7
Figure 7. Figure 7: An illustration of the confining potential and its second derivative for the Cauchy, Gaussian, and Logistic [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Here we plot Eq. (28) for the Gaussian, Logistic, and Cauchy cases. = f 2 (y) + d 2U(y) dy2 + T −1 (y)f ′ (y). (28) We evaluated this expression for the Cauchy, Gaussian, and logistic cases using a CAS, and plotted them in [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

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Works this paper leans on

69 extracted references · 45 canonical work pages

  1. [1]

    Advanced ligo

    Junaid Aasi et al. “Advanced ligo”. In: Classical and quantum gravity 32.7 (2015), p. 074001

    work page 2015

  2. [2]

    Observation of Gravitational Waves from a Binary Black Hole Merger

    B. P. Abbott et al. “Observation of Gravitational Waves from a Binary Black Hole Merger”. In: Physical Review Letters 116.6 (Feb. 2016). ISSN : 1079-7114. DOI: 10.1103/physrevlett.116.061102 . URL: http://dx. doi.org/10.1103/PhysRevLett.116.061102

    doi:10.1103/physrevlett.116.061102 2016

  3. [3]

    Properties of the Binary Black Hole Merger GW150914

    B. P. Abbott et al. “Properties of the Binary Black Hole Merger GW150914”. In: Phys. Rev. Lett. 116 (24 June 2016), p. 241102. DOI: 10.1103/PhysRevLett.116.241102 . URL: https://link.aps.org/doi/10. 1103/PhysRevLett.116.241102. 12 Efficient Bayesian Sampling with Langevin Birth-Death Dynamics A PREPRINT 30.82+0.73 −0.79 0.6 0.9 q 0.87+0.08 −0.08 0.3 0.6 d...

    doi:10.1103/physrevlett.116.241102 2016

  4. [4]

    Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo

    Rich Abbott et al. “Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo”. In: SoftwareX 13 (2021), p. 100658

    work page 2021

  5. [5]

    Population of merging compact binaries inferred using gravitational waves through GWTC-3

    Richard Abbott et al. “Population of merging compact binaries inferred using gravitational waves through GWTC-3”. In: Physical Review X 13.1 (2023), p. 011048

    work page 2023

  6. [6]

    Advanced Virgo: a second-generation interferometric gravitational wave detector

    Fausto Acernese et al. “Advanced Virgo: a second-generation interferometric gravitational wave detector”. In: Classical and Quantum Gravity 32.2 (2014), p. 024001

    work page 2014

  7. [7]

    Estimating parameters in physical models through Bayesian inversion: A complete example

    Moritz Allmaras et al. “Estimating parameters in physical models through Bayesian inversion: A complete example”. In: siam REVIEW 55.1 (2013), pp. 149–167

    work page 2013

  8. [8]

    Gravitational-wave constraints on the neutron-star-matter Equation of State

    Eemeli Annala et al. “Gravitational-wave constraints on the neutron-star-matter Equation of State”. In: Physical review letters 120.17 (2018), p. 172703

    work page 2018

Show all 69 references
  1. [9]

    Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy

    Gregory Ashton et al. “Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy”. In: The Astrophysical Journal Supplement Series 241.2 (Apr. 2019), p. 27. ISSN : 1538-4365. DOI: 10.3847/ 1538-4365/ab06fc. URL: http://dx.doi.org/10.3847/1538-4365/ab06fc

    2019 doi

  2. [10]

    Gravitational-wave physics and astronomy in the 2020s and 2030s

    Matthew Bailes et al. “Gravitational-wave physics and astronomy in the 2020s and 2030s”. In: Nature Reviews Physics 3.5 (2021), pp. 344–366

    2021

  3. [11]

    PyCBC Inference: A Python-based parameter estimation toolkit for com- pact binary coalescence signals

    Christopher Michael Biwer et al. “PyCBC Inference: A Python-based parameter estimation toolkit for com- pact binary coalescence signals”. In: Publications of the Astronomical Society of the Pacific 131.996 (2019), p. 024503

    2019

  4. [12]

    Jax: Autograd and xla

    James Bradbury et al. “Jax: Autograd and xla”. In: Astrophysics Source Code Library (2021), ascl–2111

    2021

  5. [13]

    T. A. Callister. A Thesaurus for Common Priors in Gravitational-Wave Astronomy. 2021. arXiv: 2104.09508 [gr-qc]. URL: https://arxiv.org/abs/2104.09508

    2021 arXiv

  6. [14]

    Stan: A Probabilistic Programming Language

    Bob Carpenter et al. “Stan: A Probabilistic Programming Language”. In: Journal of Statistical Software 76.1 (2017), pp. 1–32. DOI: 10.18637/jss.v076.i01

    2017 doi

  7. [15]

    Log-Concave Sampling

    Sinho Chewi. Log-Concave Sampling. Unfinished draft. Available at https://chewisinho.github.io/ main.pdf. CIRM / MIT, 2025

    2025

  8. [16]

    Parameter estimation with gravitational waves

    Nelson Christensen and Renate Meyer. “Parameter estimation with gravitational waves”. In: Reviews of Modern Physics 94.2 (Apr. 2022). ISSN : 1539-0756. DOI: 10.1103/revmodphys.94.025001 . URL: http://dx. doi.org/10.1103/RevModPhys.94.025001

    2022 doi

  9. [17]

    CPNest: A Nested Sampling Implementation for Parameter Estimation

    Walter Del Pozzo and John Veitch. CPNest: A Nested Sampling Implementation for Parameter Estimation . https://zenodo.org/records/6460935. 2022

    2022

  10. [18]

    Parallel tempering: Theory, applications, and new perspectives

    David J Earl and Michael W Deem. “Parallel tempering: Theory, applications, and new perspectives”. In: Phys- ical Chemistry Chemical Physics 7.23 (2005), pp. 3910–3916

    2005

  11. [19]

    Thomas D. P. Edwards et al. ripple: Differentiable and Hardware-Accelerated Waveforms for Gravitational Wave Data Analysis. 2023. arXiv: 2302.05329 [astro-ph.IM]. URL: https://arxiv.org/abs/2302. 05329

    2023 arXiv

  12. [20]

    Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses: Multimodal nested sampling

    F. Feroz and M. P. Hobson. “Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses: Multimodal nested sampling”. In: Monthly Notices of the Royal Astronomical Society 384.2 (Jan. 2008), pp. 449–463. IS...

    2008

  13. [21]

    MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics

    Farhan Feroz, MP Hobson, and Michael Bridges. “MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics”. In: Monthly Notices of the Royal Astronomical Society 398.4 (2009), pp. 1601–1614

    2009

  14. [22]

    Langevin diffusions on the torus: estimation and applications

    Eduardo Garc ´ıa-Portugu´es et al. “Langevin diffusions on the torus: estimation and applications”. In: Statistics and Computing 29.1 (Nov. 2017), pp. 1–22. ISSN : 1573-1375. DOI: 10.1007/s11222- 017- 9790- 2. URL: http://dx.doi.org/10.1007/s11222-017-9790-2

    2017 doi

  15. [23]

    Large sample analysis of the median heuris- tic

    Damien Garreau, Wittawat Jitkrittum, and Motonobu Kanagawa. “Large sample analysis of the median heuris- tic”. In: arXiv preprint arXiv:1707.07269 (2017)

    2017 arXiv

  16. [24]

    Ensemble samplers with affine invariance

    Jonathan Goodman and Jonathan Weare. “Ensemble samplers with affine invariance”. In: Communications in applied mathematics and computational science 5.1 (2010), pp. 65–80

    2010

  17. [25]

    Mirrored Langevin Dynamics

    Ya-Ping Hsieh et al. Mirrored Langevin Dynamics . 2020. arXiv: 1802 . 10174 [cs.LG]. URL: https : / / arxiv.org/abs/1802.10174

    2020 arXiv

  18. [26]

    Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal

    Sascha Husa et al. “Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal”. In:Phys. Rev. D93 (4 Feb. 2016), p. 044006.DOI: 10.1103/ PhysRevD.93.044006. URL: https://link.aps.org/doi/10.1103/PhysRevD.9...

    2016 doi

  19. [27]

    GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors

    Francesco Iacovelli et al. “GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors”. In: The Astrophysical Journal Supplement Series 263.1 (Oct. 2022), p. 2. ISSN : 1538-4365. DOI: 10 . 3847 / 1538 - 4365 / ac9129. URL: http : / / dx ...

    2022

  20. [28]

    Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era

    Sebastian Khan et al. “Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era”. In: Phys. Rev. D 93 (4 Feb. 2016), p. 044007. DOI: 10.1103/PhysRevD.93.044007. URL: https://link.aps.org/doi/10.1103...

    2016 doi

  21. [29]

    Recent observations of gravitational waves by LIGO and Virgo detectors

    Andrzej Kr ´olak and Paritosh Verma. “Recent observations of gravitational waves by LIGO and Virgo detectors”. In: Universe 7.5 (2021), p. 137

    2021

  22. [30]

    Ensemble preconditioning for Markov chain Monte Carlo simulation

    Benedict Leimkuhler, Charles Matthews, and Jonathan Weare. “Ensemble preconditioning for Markov chain Monte Carlo simulation”. In: Statistics and Computing 28 (2018), pp. 277–290

    2018

  23. [31]

    Langevin Birth-death

    Leviyev. Langevin Birth-death. https://github.com/leviyevalex/langevin_birth_death. 2025

    2025

  24. [32]

    hybrid rosenbrock: An implementation of the n-dimensional Rosenbrock distribution for MCMC testing

    Alex Leviyev. hybrid rosenbrock: An implementation of the n-dimensional Rosenbrock distribution for MCMC testing. GitHub repository. 2025. URL: https://github.com/leviyevalex/hybrid_rosenbrock

    2025

  25. [33]

    The Mirror Langevin Algorithm Converges with Vanishing Bias

    Ruilin Li et al. The Mirror Langevin Algorithm Converges with Vanishing Bias . 2021. arXiv: 2109 . 12077 [cs.DS]. URL: https://arxiv.org/abs/2109.12077

    2021 arXiv

  26. [34]

    Ensemble Markov chain Monte Carlo with teleporting walkers

    Michael Lindsey, Jonathan Weare, and Anna Zhang. “Ensemble Markov chain Monte Carlo with teleporting walkers”. In: SIAM/ASA Journal on Uncertainty Quantification 10.3 (2022), pp. 860–885

    2022

  27. [35]

    The mathematical engineering of deep learning

    Benoit Liquet, Sarat Moka, and Yoni Nazarathy. The mathematical engineering of deep learning. 2024

    2024

  28. [36]

    Stein variational gradient descent: A general purpose bayesian inference algo- rithm

    Qiang Liu and Dilin Wang. “Stein variational gradient descent: A general purpose bayesian inference algo- rithm”. In: Advances in neural information processing systems 29 (2016)

    2016

  29. [37]

    Accelerating langevin sampling with birth-death

    Yulong Lu, Jianfeng Lu, and James Nolen. “Accelerating langevin sampling with birth-death”. In:arXiv preprint arXiv:1905.09863 (2019)

    1905 arXiv

  30. [38]

    Yi-An Ma, Tianqi Chen, and Emily B. Fox. A Complete Recipe for Stochastic Gradient MCMC . 2015. arXiv: 1506.04696 [math.ST]. URL: https://arxiv.org/abs/1506.04696

    2015 arXiv

  31. [39]

    GWpy: A Python package for gravitational-wave astrophysics

    D. M. Macleod et al. “GWpy: A Python package for gravitational-wave astrophysics”. In: SoftwareX 13 (2021), p. 100657. ISSN : 2352-7110. DOI: 10.1016/j.softx.2021.100657. URL: https://www.sciencedirect. com/science/article/pii/S2352711021000029

    2021

  32. [40]

    Gravitational Waves

    Michele Maggiore. Gravitational Waves. Vol. 1: Theory and Experiments. Oxford University Press, 2007.ISBN : 978-0-19-171766-6, 978-0-19-852074-0. DOI: 10.1093/acprof:oso/9780198570745.001.0001

    2007

  33. [41]

    Directional statistics

    Kanti V Mardia and Peter E Jupp. Directional statistics. John Wiley & Sons, 2009

    2009

  34. [42]

    A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion

    James Martin et al. “A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion”. In: SIAM Journal on Scientific Computing 34.3 (2012), A1460–A1487

    2012

  35. [43]

    Sampling from multimodal distributions using tempered transitions

    Radford M Neal. “Sampling from multimodal distributions using tempered transitions”. In: Statistics and com- puting 6 (1996), pp. 353–366

    1996

  36. [44]

    Numerical optimization

    Jorge Nocedal and Stephen J Wright. Numerical optimization. Springer, 1999

    1999

  37. [45]

    An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing

    Filippo Pagani, Martin Wiegand, and Saralees Nadarajah. “An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing”. In: Scandinavian Journal of Statistics 49.2 (2022), pp. 657–680

    2022

  38. [46]

    Sampling rare event energy landscapes via birth-death augmented dynamics

    Benjamin Pampel et al. “Sampling rare event energy landscapes via birth-death augmented dynamics”. In: Phys. Rev. E 107 (2 Feb. 2023), p. 024141. DOI: 10.1103/PhysRevE.107.024141 . URL: https://link.aps. org/doi/10.1103/PhysRevE.107.024141

    2023 doi

  39. [47]

    hyppo: A Comprehensive Multivariate Hypothesis Testing Python Package

    Sambit Panda et al. hyppo: A Comprehensive Multivariate Hypothesis Testing Python Package . 2020. arXiv: 1907.02088 [stat.CO]

    2020 arXiv

  40. [48]

    Stochastic processes and applications

    Grigorios A Pavliotis. “Stochastic processes and applications”. In: Texts in applied mathematics 60 (2014)

    2014

  41. [49]

    A Hamiltonian Monte–Carlo method for Bayesian inference of supermas- sive black hole binaries

    Edward K Porter and J ´erˆome Carr´e. “A Hamiltonian Monte–Carlo method for Bayesian inference of supermas- sive black hole binaries”. In: Classical and Quantum Gravity 31.14 (2014), p. 145004

    2014

  42. [50]

    The metropolis—hastings algorithm

    Christian P Robert et al. “The metropolis—hastings algorithm”. In: Monte Carlo statistical methods (2004), pp. 267–320

    2004

  43. [51]

    Removing degeneracy and multimodality in gravitational wave source parameters

    Javier Roulet et al. “Removing degeneracy and multimodality in gravitational wave source parameters”. In: Physical Review D 106.12 (2022), p. 123015

    2022

  44. [52]

    Sampling with mirrored stein operators

    Jiaxin Shi, Chang Liu, and Lester Mackey. “Sampling with mirrored stein operators”. In: arXiv preprint arXiv:2106.12506 (2021)

    2021 arXiv

  45. [53]

    Nested sampling for general Bayesian computation

    John Skilling. “Nested sampling for general Bayesian computation”. In: (2006). 15 Efficient Bayesian Sampling with Langevin Birth-Death Dynamics A PREPRINT

    2006

  46. [54]

    Massively parallel Bayesian inference for transient gravitational-wave astronomy

    Rory J E Smith et al. “Massively parallel Bayesian inference for transient gravitational-wave astronomy”. In: Monthly Notices of the Royal Astronomical Society 498.3 (Aug. 2020), pp. 4492–4502. ISSN : 1365-2966. DOI: 10.1093/mnras/staa2483. URL: http://dx.doi.org/10.1093/mnras...

    2020 doi

  47. [55]

    dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and ev- idences

    Joshua S Speagle. “dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and ev- idences”. In: Monthly Notices of the Royal Astronomical Society 493.3 (Feb. 2020), pp. 3132–3158. ISSN : 1365-2966. DOI: 10.1093/mnras/staa278. URL: http://dx.doi.org/10.10...

    2020 doi

  48. [56]

    Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme

    Saifuddin Syed et al. “Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme”. In: Journal of the Royal Statistical Society Series B: Statistical Methodology84.2 (Dec. 2021), pp. 321–350. ISSN : 1467-9868. DOI: 10.1111/rssb.12464. URL: http://dx.doi.org/10....

    2021 doi

  49. [57]

    Energy statistics: A class of statistics based on distances

    G ´abor J Sz´ekely and Maria L Rizzo. “Energy statistics: A class of statistics based on distances”. In: Journal of statistical planning and inference 143.8 (2013), pp. 1249–1272

    2013

  50. [58]

    An introduction to Bayesian inference in gravitational-wave astronomy: Pa- rameter estimation, model selection, and hierarchical models

    Eric Thrane and Colm Talbot. “An introduction to Bayesian inference in gravitational-wave astronomy: Pa- rameter estimation, model selection, and hierarchical models”. In: Publications of the Astronomical Society of Australia 36 (2019). ISSN : 1448-6083. DOI: 10.1017/pasa.2019...

    2019 doi

  51. [59]

    Optimal Preconditioning and Fisher Adaptive Langevin Sampling

    Michalis Titsias. “Optimal Preconditioning and Fisher Adaptive Langevin Sampling”. In: Advances in Neural Information Processing Systems 36 (2024)

    2024

  52. [60]

    Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects

    Michele Vallisneri. “Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects”. In: Physical Review D—Particles, Fields, Gravitation, and Cosmology 77.4 (2008), p. 042001

    2008

  53. [61]

    Parameter estimation for compact binaries with ground-based gravitational-wave observa- tions using the LALInference software library

    John Veitch et al. “Parameter estimation for compact binaries with ground-based gravitational-wave observa- tions using the LALInference software library”. In: Physical Review D 91.4 (2015), p. 042003

    2015

  54. [62]

    Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices

    Santosh Vempala and Andre Wibisono. “Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices”. In: Advances in neural information processing systems 32 (2019)

    2019

  55. [63]

    SciPy 1.0: fundamental algorithms for scientific computing in Python

    Pauli Virtanen et al. “SciPy 1.0: fundamental algorithms for scientific computing in Python”. In: Nature methods 17.3 (2020), pp. 261–272

    2020

  56. [64]

    Bayesian inference in physics

    Udo V on Toussaint. “Bayesian inference in physics”. In: Reviews of Modern Physics 83.3 (2011), pp. 943–999

    2011

  57. [65]

    Stein Variational Gradient Descent With Matrix-Valued Kernels

    Dilin Wang et al. Stein Variational Gradient Descent With Matrix-Valued Kernels. 2019. arXiv: 1910.12794 [stat.ML]. URL: https://arxiv.org/abs/1910.12794

    2019 arXiv

  58. [66]

    Tikhonov or lasso regularization: Which is better and when

    Fei Wang, Sanjay Chawla, and Wei Liu. “Tikhonov or lasso regularization: Which is better and when”. In: 2013 IEEE 25th International Conference on Tools with Artificial Intelligence. IEEE. 2013, pp. 795–802

    2013

  59. [67]

    Applied stochastic analysis

    E Weinan, Tiejun Li, and Eric Vanden-Eijnden. Applied stochastic analysis. V ol. 199. American Mathematical Soc., 2021

    2021

  60. [68]

    Kaze W. K. Wong, Maximiliano Isi, and Thomas D. P. Edwards. Fast gravitational wave parameter estimation without compromises. 2023. arXiv: 2302.05333 [astro-ph.IM]. URL: https://arxiv.org/abs/2302. 05333

    2023 arXiv

  61. [69]

    Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays

    Nicol ´as Yunes and Xavier Siemens. “Gravitational-wave tests of general relativity with ground-based detectors and pulsar-timing arrays”. In: Living Reviews in Relativity 16.1 (2013), pp. 1–124. A Efficient Birth-Death Implementation The birth-death process described in Algor...

    2013

Pith tools

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