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Bayesian pulsar timing and noise analysis with Vela.jl: an overview

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Independent pulsar-timing code reproduces existing results to 10 ns

desk verdict A solid software paper for a new Bayesian pulsar timing package, with one honest caveat: the cheat-prior robustness check is asserted in prose but not shown, so the Bayesian validation is weaker than it could be. read the letter →

arxiv 2412.15858 v4 pith:JRU225WS submitted 2024-12-20 astro-ph.IM astro-ph.HE

Abhimanyu Susobhanan This is my paper · ORCID
classification astro-ph.IMastro-ph.HE
keywords pulsartimingBayesianinferencenoiseanalysisJuliaarraysnestedsamplingMarkovchainMonteCarlonarrowband
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

This paper presents Vela.jl, a Julia package for Bayesian pulsar timing and noise analysis, along with pyvela, a Python binding. It aims to establish that a from-scratch implementation of the full non-linear timing and noise model can be efficient, parallel, and accurate enough for routine single-pulsar use and for the large datasets of pulsar timing arrays. The evidence comes in two forms: timing residuals that agree with two established pulsar-timing packages at the ~10 ns level, and Bayesian posterior runs on simulated datasets that agree with an established fitter and recover injected parameters. A practical benefit is that Bayesian noise characterization no longer has to be separated from the full timing-model fit, and can be run with whatever sampler the user prefers.

What carries the argument

The load-bearing machinery is a modular, from-scratch implementation of the timing and noise model: TOA delays and phase corrections are represented as Component objects, each with a correction routine, and the log-likelihood is assembled by a Kernel object that evaluates the Gaussian likelihood in equation (4). Computational cost is controlled by a reduced-rank covariance model together with the Woodbury and matrix-determinant lemmas, and by an ECORR block decomposition that evaluates the correlated-noise likelihood in linear time. Numerically, TOA values and rotational phases use the Double64 extended-precision representation, while other quantities use ordinary double precision; the rotational frequency is stored as a sum of two doubles to keep the parameter type uniform. Red-noise Fourier coefficients are reparameterised by their prior standard deviations so they are a priori unit-normal, which avoids hard-to-sample funnel geometries.

What would settle it

Run the same two simulated datasets through Vela.jl with broad priors anchored to physical ranges rather than to the reference fitter's point estimates (e.g., flat priors tens to thousands of times wider than the quoted uncertainties), and check whether the posterior medians and the reference-fitter agreement survive; if they shift beyond the quoted uncertainties, the circular-analysis concern is confirmed.

Watch

Extended reading notes

Core claim

On its own terms, this paper claims that Vela.jl delivers an independent, efficient, parallelized implementation of the full non-linear pulsar timing and noise model, with a Python binding called pyvela. The evidence is threefold: timing residuals computed by Vela.jl agree with those from PINT and tempo2 to within about 10 ns for an identical model; a small simulated dataset yields posterior distributions that agree with pint.bayesian; and a larger simulated binary-pulsar dataset with injected dispersion-measure variations recovers astrometric and binary parameters within 3 sigma. The larger example also shows a limitation the paper concedes: some dispersion-measure parameters do not recover their injected values, attributed to the DM model not capturing short-timescale variations.

Load-bearing premise

The load-bearing premise is that the validation posteriors are not steered by 'cheat' priors centered on the very estimates being reproduced -- a risk the paper acknowledges and says it checked by widening the priors, but only asserts in prose, without reporting the numbers.

Editorial extensions

If this is right

  • Bayesian inference over the full non-linear timing and noise model becomes available with any MCMC or nested sampler, including Python samplers through pyvela.
  • The reported ~10 ns residual agreement provides an independent numerical cross-check of existing timing-model implementations, at roughly the level at which those implementations already agree with each other.
  • Multi-threaded, linear-time likelihood evaluation makes full Bayesian noise characterization practical on the hundreds-of-TOAs datasets typical of current pulsar timing array pulsars.
  • Single-pulsar PTA analyses no longer need to choose between linearized analytic marginalisation and a full non-linear sampler locked to one sampling engine.
  • The same modular component-and-kernel design can carry future wideband and photon-domain timing without restructuring the likelihood machinery.

Reading between the lines

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

  • If the prior-widening check were reported quantitatively, the cheat-prior validation could be retired for these datasets; until then, the posterior agreement shown should be read as conditional on those priors.
  • The linear-time likelihood evaluation opens a practical benchmark: running per-pulsar noise characterization for an entire pulsar timing array on a single workstation, which the paper does not itself demonstrate.
  • The sampler-agnostic interface makes model comparison by Bayesian evidence a direct next step, since nested sampling can be run without porting Vela.jl into a specific engine.
  • If the planned wideband and photon-domain timing are added, the same component-and-kernel architecture could unify narrowband, wideband, and high-energy pulsar timing analysis in one package.
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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 presents Vela.jl, a Julia package for Bayesian pulsar timing and noise analysis, together with a Python binding called pyvela. Vela.jl implements the nonlinear timing and noise model independently, using PINT only for file input, clock corrections, and solar system ephemeris computations. The manuscript describes the package architecture, numerical-precision choices, component types, prior handling, likelihood kernels, and two validation examples: a residual comparison against PINT and tempo2 at the ~10 ns level, and posterior comparisons against pint.bayesian on a small simulated dataset and on a larger simulated J1909-3744 dataset. The paper argues that Vela.jl is an efficient, modular, and reliable alternative to TEMPONEST and a complement to ENTERPRISE.

Significance. If the central claims are borne out, Vela.jl would be a useful independent tool for Bayesian pulsar timing and noise analysis, with the practical advantages of sampler-agnostic interfaces, multi-threading, and a Python binding. The paper has clear strengths: the residual comparison against PINT and tempo2 is an externally grounded check of the deterministic timing model; the design discussion (extended precision, dimensional types, component hierarchy) is informative; and the package is distributed with version control, documentation, and a test suite. The main weakness is that the Bayesian validation relies on 'cheat' priors centered on PINT maximum-likelihood values, and the stated robustness to prior width is not quantitatively documented. Because this concerns the load-bearing evidence for the likelihood and sampler implementation, the claims as presented are defensible but not yet fully supported.

major comments (3)
  1. [§4.1, §4.2, Appendix B] The Bayesian validation examples both use 'cheat' priors, uniform distributions centered on PINT maximum-likelihood estimates with widths 10–40 times the frequentist uncertainties. Appendix B itself warns that such priors 'effectively do circular analysis' when the data do not provide enough signal-to-noise. The only response in each example is the sentence 'We have checked that increasing the width of the 'cheat' priors does not appreciably alter the posterior distribution,' with no widened-prior plots, summary statistics, or quantitative comparisons. A prior that is narrow enough to concentrate near the PINT or true values can produce apparent agreement with pint.bayesian and apparent parameter recovery even if the likelihood or sampler were incorrect. Please add quantitative evidence: for example, posterior medians and credible intervals for prior widths of 10x, 40x, and 100x, overlap or distance metrics between posteriors, or at least one validation run with broad physically motivated priors.
  2. [§4.2, Figure 8] The J1909-3744 example does not cleanly validate the likelihood implementation for the correlated noise model. The data are simulated with epoch-wise DM measurements from InPTA DR1, while the fitted model uses a Taylor-series-plus-40-harmonic Gaussian-process DM model; the text admits that some estimated parameters do not agree well with the injected values and attributes this to inadequacy of the DM model. As presented, the example cannot separate model mismatch from an error in the Gaussian-process likelihood, prior transform, or sampler in the 104-dimensional parameter space. The caption's statement that astrometric and binary parameters are consistent within 3σ does not quantify the noise parameters or the Fourier coefficients. Please provide a full parameter-by-parameter coverage or z-score comparison for all free parameters, and ideally an injection-recovery test in which the data are generated from exactly the same Gaussian-process model as the fit.
  3. [§3.1] The ~10 ns residual agreement against PINT and tempo2 (Figure 1) is a credible check of the deterministic timing model, but it does not exercise the noise-model likelihood, the reduced-rank covariance expression (Eq. 5), the ECORR likelihood (Eq. C5), or the Gaussian-process prior transform (Appendix D). Because the abstract claims a full timing and noise analysis package, the Bayesian validation should include at least one comparison that isolates the stochastic likelihood, for example a comparison with ENTERPRISE or TEMPONEST on simulated data with broad priors and a single well-understood red-noise component.
minor comments (4)
  1. [§3.2] In the sentence defining the split of F0, the text reads 'F_big ≪ F_small'; this inequality appears to be inverted and should presumably be F_big ≫ F_small. Please correct it.
  2. [Figure 4] The par and tim file names in the code sample appear with inserted spaces, for example 'N GC 64 40E . par'. If these spaces are present in the actual code, the example will not run; if they are a line-wrapping artifact, please adjust the figure so the code is unambiguous.
  3. [Tables 1 and 2] The captions appear as 'T able 1' and 'T able 2' in the compiled text; please check the typesetting so the table labels are rendered correctly.
  4. [Equation (D7)] Equation (D7) is difficult to parse in the provided version: the placement of the reference frequency f_yr is ambiguous. Please ensure the equation is typeset unambiguously and define f_yr explicitly in the text.

Circularity Check

1 steps flagged · score 2.0 of 10

Validation rests on external benchmarks (PINT/tempo2 residual agreement); the only mild circular element is the 'cheat' priors centered on PINT maximum-likelihood values, with the robustness check reported only in prose.

  1. fitted input called prediction [Section 4.1 (PSR J1748-2021E), Section 4.2 (PSR J1909-3744), Appendix B]
    "'Cheat' prior distributions, i.e., uniform distributions centered at the maximum likelihood values obtained using PINT whose widths are 10 times the frequentist uncertainties, are used for all other parameters... We have checked that increasing the width of the 'cheat' priors does not appreciably alter the posterior distribution. ... Care must be taken to ensure that the data provides enough S/N for the parameter for the 'cheat' prior distribution to be valid, lest we effectively do circular analysis (Kriegeskorte et al. 2009)."

    The Bayesian validation claims agreement with pint.bayesian and recovery of injected parameters, but the priors for timing parameters are centered on the PINT maximum-likelihood estimates of the same parameters. For any parameter with insufficient signal-to-noise, the posterior will be dominated by this prior, so agreement/recovery is enforced by the prior center rather than by the Vela.jl likelihood. The paper itself concedes in Appendix B that such priors can 'effectively do circular analysis.' The only counter-evidence offered is an unquantified sentence in each example stating that widening the priors did not appreciably alter the posterior; no widened-prior plots, summary statistics, or numerical comparisons are shown.

full rationale

The paper's central claim is that Vela.jl provides an independent implementation of the full non-linear pulsar timing and noise model. The deterministic timing-model residuals are checked against two external packages (PINT and tempo2) with agreement at the ~10 ns level, which is an external, non-circular benchmark. The noise-model likelihood and sampler are validated on two simulated datasets, and this is where the mild circularity lies: the 'cheat' priors are centered on PINT maximum-likelihood estimates, so the posterior agreement with pint.bayesian could in part be inherited from the common prior rather than from a correct likelihood. However, the paper explicitly identifies this risk in Appendix B and states that widening the priors does not change the posteriors. Although that robustness check is not quantified, the admission plus the external residual agreement keeps the work from being fundamentally circular. Self-citations to the author's PINT-related papers are used for data generation and clock/ephemeris precomputations, not as load-bearing justification for Vela.jl's correctness. Overall: no significant circularity; one mild, acknowledged prior-centered validation element. Score 2.0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim is that Vela.jl correctly implements the established pulsar timing and noise model. The implementation relies on standard timing model equations, Gaussian process noise representations, and Double64 precision. The validation examples introduce hand-chosen analysis settings (cheat prior widths, number of Fourier harmonics) which are tested for robustness. No new physical entities are posited.

free parameters (2)
  • Cheat prior width multipliers = 10x (J1748-2021E) and 40x (J1909-3744) frequentist uncertainties
    Chosen by hand in Section 4 and Appendix B. The posterior agreement between Vela.jl and pint.bayesian could be artificially inflated if these priors are too narrow. The authors report that widening them does not change results, which mitigates the dependence.
  • Number of DM noise Fourier harmonics (Nharm) = 40
    Chosen for the J1909-3744 example (Section 4.2). The authors note the DM model may not capture short-timescale DM variations, which they link to the disagreement of some injected parameters.
assumptions (4)
  • domain assumption Standard pulsar timing model equations (Eqs. 1-2): TOA delays (binary, dispersion, solar system, clock) and phase evolution with spin frequency derivatives, glitches, etc.
    Invoked in Section 2 as the mathematical model Vela.jl implements; assumed correct and complete for narrowband timing.
  • standard math Gaussian-process representation of correlated noise with reduced-rank covariance C = N + U^T Phi U (Eq. 5) and Woodbury/determinant lemmas for efficient computation.
    Used in Section 2 and Appendix D; standard linear algebra results.
  • domain assumption Phase-connected timing solution and immutable TOA collections are available (Section 3.3).
    This allows precomputing pulse numbers and converting flags to bit masks; if TOAs change or are added, Vela.jl's representation may need rebuilding.
  • domain assumption Double64 extended-precision arithmetic is sufficient to represent TOAs and phases accurately.
    Section 3.1 assumes Double64 gives the needed precision; the ~10 ns agreement with PINT/tempo2 is the empirical support.

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Cite this review

Pith. "Pith review of Bayesian pulsar timing and noise analysis with Vela.jl: an overview." pith.science (2026). https://pith.science/paper/JRU225WS

@misc{pith2026241215858,
  author       = {Pith},
  title        = {Pith review of: Bayesian pulsar timing and noise analysis with Vela.jl: an overview},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRU225WS}},
  note         = {Machine review of arXiv:2412.15858}
}
read the original abstract

We present Vela, an efficient, modular, easy-to-use Bayesian pulsar timing and noise analysis package written in Julia. Vela provides an independent, efficient, and parallelized implementation of the full non-linear pulsar timing and noise model along with a Python binding named pyvela. One-time operations such as data file input, clock corrections, and solar system ephemeris computations are performed by pyvela with the help of the PINT pulsar timing package. Its reliability is ensured via careful design utilizing Julia's type system, strict version control, and an exhaustive test suite. This paper describes the design and usage of Vela focusing on the narrowband paradigm.

Figures

Figures reproduced from arXiv: 2412.15858 by the authors.

Figure 1
Figure 1. Absolute difference between the timing residuals computed using Vela.jl, PINT, and tempo2 for the same timing & noise model given identical model parameters. The dataset used herein corresponds to PSR J1748−2021E (Freire et al. 2008) and is distributed as an example along with PINT. See subsection 4.1 for more details. The three packages agree within ∼ 10 ns level. by the DoubleFloats.jl package (Sarnoff et al. 2022… view at source ↗
Figure 2
Figure 2. The structure of the TOA type. ‘::’ represents ‘is instance of’. TOA.value is in the TDB timescale. The SolarSystemEphemeris type contains 3-tuples representing the position and velocity of the observatory with respect to the SSB (SolarSystemEphemeris.ssb obs pos and SolarSystemEphemeris.ssb obs vel), and the positions of various solar sys￾tem objects with respect to the observatory. The clock corrections required f… view at source ↗
Figure 3
Figure 3. The structure of the TimingModel type. ‘::’ represents ‘is instance of’. pulsar name stores the name of the pulsar. ephem is the name of the solar system ephemeris model. clock is the name of the realization of the TT timescale used in clock corrections (e.g., TT(BIPM2021)); see Hobbs et al. (2006). units is the timescale of TOA.value (only TDB is supported). epoch is the rotational frequency epoch. The components t… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: An example code snippet demonstrating the pyvela interface with the MCMC sampler emcee. User-defined priors are read from a JSON file (see Appendix B). The emcee.EnsembleSampler object is initialized with samples drawn from the prior distribution with the help of SPNTA…
Figure 5
Figure 5. Figure 5: An example code snippet demonstrating the pyvela interface with the nested sampler nestle. method="multi" invokes the MultiNest algorithm (Feroz et al. 2009) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: A schematic diagram summarizing Vela.jl’s architecture. Components, Kernel, Priors, and ParamHandler are parts of the TimingModel. Parameter Description Prior M2 Companion mass (M⊙) Uniform distribution around the IPTA DR2 measurement with width 40 times the correspond…
Figure 7
Figure 7. Figure 7: Bayesian timing & noise analysis results for a simulated dataset of PSR J1748−2021E. The plotted parameters are source coordinates (RAJ, DECJ), overall phase offset (PHOFF), dispersion measure (DM), rotational phase and its derivative (F0, F1), and a global EFAC (EFAC1…
Figure 8
Figure 8. Figure 8: Bayesian timing & noise analysis results for a simulated dataset of PSR J1909-3744. The plotted parameters are parallax (PX), proper motion (PMRA, PMDEC), orbital period (PB), projected semi-major axis of the pulsar orbit (A1), companion mass (M2), sine-inclination (SI…
Figure 9
Figure 9. Figure 9: The hierarchy of Component base types. See [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: An example of the user-defined prior distributions represented in the JSON format. ‘distribution’ should be a distribution available in the Distributions.jl package (Besan¸con et al. 2021). ‘args’ contains the arguments to construct a distribution object. The ‘upper’ …

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. PSRDISP: A novel approach to modeling dispersive processes in single-pulsar noise analysis using epoch-wise dispersion measures

    astro-ph.IM 2026-07 unverdicted novelty 6.0 of 10

    PSRDISP is a Gaussian-process framework that fits dispersion-measure and solar-wind noise directly to epoch-wise dispersion measures, recovering injected signals in simulated pulsar data.

Reference graph

Works this paper leans on

87 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    z ^ ^R˕cpP 60: 6d.56V X ib m(7eu

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    work page arXiv 2021

  4. [4]

    M., et al

    Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023 a , The Astrophysical Journal Letters, 951, L10, 10.3847/2041-8213/acda88

    doi:10.3847/2041-8213/acda88 2023

  5. [5]

    2023 b , The Astrophysical Journal Letters, 951, L8, 10.3847/2041-8213/acdac6

    ---. 2023 b , The Astrophysical Journal Letters, 951, L8, 10.3847/2041-8213/acdac6

    doi:10.3847/2041-8213/acdac6 2023

  6. [6]

    2024, The Astrophysical Journal, 966, 105, 10.3847/1538-4357/ad36be

    Agazie , G., Antoniadis , J., Anumarlapudi , A., et al. 2024, The Astrophysical Journal, 966, 105, 10.3847/1538-4357/ad36be

    doi:10.3847/1538-4357/ad36be 2024

  7. [7]

    B., Baldini , L., et al

    Ajello , M., Atwood , W. B., Baldini , L., et al. 2022, Science, 376, 521, 10.1126/science.abm3231

    doi:10.1126/science.abm3231 2022

  8. [8]

    F., Arzoumanian , Z., Baker , P

    Alam , M. F., Arzoumanian , Z., Baker , P. T., et al. 2021, The Astrophysical Journals, 252, 5, 10.3847/1538-4365/abc6a1

    doi:10.3847/1538-4365/abc6a1 2021

Show all 87 references
  1. [9]

    Antonelli , M., Montoli , A., & Pizzochero , P. M. 2022, in Astrophysics in the XXI Century with Compact Stars. Edited by C.A.Z. Vasconcellos. eISBN 978-981-12-2094-4. Singapore: World Scientific, ed. C. A. Z. Vasconcellos (World Scientific), 219--281, 10.1142/9789811220944_0007

    2022 doi

  2. [10]

    2015, The Astrophysical Journal, 813, 65, 10.1088/0004-637X/813/1/65

    Arzoumanian, Z., Brazier, A., Burke-Spolaor, S., et al. 2015, The Astrophysical Journal, 813, 65, 10.1088/0004-637X/813/1/65

    2015 doi

  3. [11]

    S., & Taylor , J

    Arzoumanian , Z., Fruchter , A. S., & Taylor , J. H. 1994, The Astrophysical Journall, 426, L85, 10.1086/187346

    1994 doi

  4. [12]

    2022, Nature Reviews Methods Primers, 2, 39, 10.1038/s43586-022-00121-x

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

    2022 doi

  5. [13]

    C., & Hellings , R

    Backer , D. C., & Hellings , R. W. 1986, Annual Review of Astronomy and Astrophysics, 24, 537, 10.1146/annurev.aa.24.090186.002541

    1986

  6. [14]

    2021, nestle: Nested sampling algorithms for evaluating Bayesian evidence

    Barbary, K. 2021, nestle: Nested sampling algorithms for evaluating Bayesian evidence . http://kylebarbary.com/nestle/

    2021

  7. [15]

    2021, Journal of Statistical Software, 98, 1, 10.18637/jss.v098.i16

    Besançon, M., Papamarkou, T., Anthoff, D., et al. 2021, Journal of Statistical Software, 98, 1, 10.18637/jss.v098.i16

    2021 doi

  8. [16]

    Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. 2017, SIAM R eview, 59, 65, 10.1137/141000671

    2017 doi

  9. [17]

    N., Guo, Y

    Chen, S., Caballero, R. N., Guo, Y. J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 508, 4970, 10.1093/mnras/stab2833

    2021 doi

  10. [18]

    T., Fonseca , E., Ransom , S

    Cromartie , H. T., Fonseca , E., Ransom , S. M., et al. 2020, Nature Astronomy, 4, 72, 10.1038/s41550-019-0880-2

    2020 doi

  11. [19]

    1986, Annales de L'Institut Henri Poincare Section (A) Physique Theorique, 44, 263

    Damour , T., & Deruelle , N. 1986, Annales de L'Institut Henri Poincare Section (A) Physique Theorique, 44, 263. http://www.numdam.org/item/AIHPA_1986__44_3_263_0/

    1986

  12. [20]

    1971, Numerische Mathematik, 18, 224

    Dekker, T. 1971, Numerische Mathematik, 18, 224. http://eudml.org/doc/132105

    1971

  13. [21]

    T., Vigeland , S

    Deller , A. T., Vigeland , S. J., Kaplan , D. L., et al. 2016, The Astrophysical Journal, 828, 8, 10.3847/0004-637X/828/1/8

    2016 doi

  14. [22]

    2009, Bulletin of the American Mathematical Society, 46, 179textendash205, 10.1090/S0273-0979-08-01238-X

    Diaconis, P. 2009, Bulletin of the American Mathematical Society, 46, 179textendash205, 10.1090/S0273-0979-08-01238-X

    2009 doi

  15. [24]

    2017, PAL2 (PTA Algorithm Library)

    Ellis, J., & van Haasteren, R. 2017, PAL2 (PTA Algorithm Library). https://github.com/jellis18/PAL2

    2017

  16. [25]

    B., & Wahlquist, H

    Estabrook, F. B., & Wahlquist, H. D. 1975, General Relativity and Gravitation, 6, 439, 10.1007/BF00762449

    1975 doi

  17. [26]

    P., & Bridges, M

    Feroz, F., Hobson, M. P., & Bridges, M. 2009, Mon. Not. Roy. Astron. Soc., 398, 1601, 10.1111/j.1365-2966.2009.14548.x

    2009

  18. [27]

    2016, The Journal of Open Source Software, 1, 24, 10.21105/joss.00024

    Foreman-Mackey, D. 2016, The Journal of Open Source Software, 1, 24, 10.21105/joss.00024

    2016 doi

  19. [28]

    W., Lang , D., & Goodman , J

    Foreman-Mackey , D., Hogg , D. W., Lang , D., & Goodman , J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306, 10.1086/670067

    2013 doi

  20. [29]

    S., & Backer , D

    Foster , R. S., & Backer , D. C. 1990, The Astrophysical Journal, 361, 300, 10.1086/169195

    1990 doi

  21. [30]

    E., Johnson , A

    Freedman , G. E., Johnson , A. D., van Haasteren , R., & Vigeland , S. J. 2023, Physical Review D, 107, 043013, 10.1103/PhysRevD.107.043013

    2023 doi

  22. [31]

    Freire , P. C. C., Ransom , S. M., B \'e gin , S., et al. 2008, The Astrophysical Journal, 675, 670, 10.1086/526338

    2008 doi

  23. [32]

    Freire , P. C. C., & Wex , N. 2010, Monthly Notices of the Royal Astronomical Society, 409, 199, 10.1111/j.1365-2966.2010.17319.x

    2010

  24. [33]

    2020, Monthly Notices of the Royal Astronomical Society, 497, 3264, 10.1093/mnras/staa2081

    Goncharov, B., Zhu, X.-J., & Thrane, E. 2020, Monthly Notices of the Royal Astronomical Society, 497, 3264, 10.1093/mnras/staa2081

    2020 doi

  25. [34]

    1996, Parallel Computing, 22, 789, https://doi.org/10.1016/0167-8191(96)00024-5

    Gropp, W., Lusk, E., Doss, N., & Skjellum, A. 1996, Parallel Computing, 22, 789, https://doi.org/10.1016/0167-8191(96)00024-5

    1996 doi

  26. [35]

    J., Hobson , M

    Handley , W. J., Hobson , M. P., & Lasenby , A. N. 2015, Monthly Notices of the Royal Astronomical Society, 450, L61, 10.1093/mnrasl/slv047

    2015 doi

  27. [36]

    H., & Rickett , B

    Hankins , T. H., & Rickett , B. J. 1986, The Astrophysical Journal, 311, 684, 10.1086/164807

    1986 doi

  28. [37]

    R., Millman , K

    Harris , C. R., Millman , K. J., van der Walt , S. J., et al. 2020, Nature, 585, 357, 10.1038/s41586-020-2649-2

    2020 doi

  29. [38]

    S., Simon, J., Madison, D

    Hazboun, J. S., Simon, J., Madison, D. R., et al. 2022, The Astrophysical Journal, 929, 39, 10.3847/1538-4357/ac5829

    2022 doi

  30. [39]

    W., & Downs , G

    Hellings , R. W., & Downs , G. S. 1983, The Astrophysical Journall, 265, L39, 10.1086/183954

    1983 doi

  31. [40]

    A., & Stinebring , D

    Hemberger , D. A., & Stinebring , D. R. 2008, The Astrophysical Journall, 674, L37, 10.1086/528985

    2008 doi

  32. [41]

    2014, TEMPO2 examples

    Hobbs, G. 2014, TEMPO2 examples. https://www.jb.man.ac.uk/ pulsar/Resources/tempo2_examples_ver1.pdf

    2014

  33. [42]

    B., Edwards , R

    Hobbs , G. B., Edwards , R. T., & Manchester , R. N. 2006, Monthly Notices of the Royal Astronomical Society, 369, 655, 10.1111/j.1365-2966.2006.10302.x

    2006

  34. [43]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, 10.1109/MCSE.2007.55

    2007 doi

  35. [44]

    2018, arXiv e-prints, arXiv:1810.07951, 10.48550/arXiv.1810.07951

    Innes , M. 2018, arXiv e-prints, arXiv:1810.07951, 10.48550/arXiv.1810.07951

    2018 doi arXiv

  36. [45]

    D., Meyers , P

    Johnson , A. D., Meyers , P. M., Baker , P. T., et al. 2024, Physical Review D, 109, 103012, 10.1103/PhysRevD.109.103012

    2024 doi

  37. [46]

    L., Stovall, K., van Kerkwijk, M

    Kaplan, D. L., Stovall, K., van Kerkwijk, M. H., Fremling, C., & Istrate, A. G. 2018, The Astrophysical Journal, 864, 15, 10.3847/1538-4357/aad54c

    2018 doi

  38. [47]

    2009, in IAU Symposium \#261, American Astronomical Society, Vol

    Klioner , S., Capitaine , N., Folkner , W., et al. 2009, in IAU Symposium \#261, American Astronomical Society, Vol. 41, 883, 10.48550/arXiv.0907.5100

    2009 doi arXiv

  39. [48]

    Kopeikin , S. M. 1995, The Astrophysical Journal Letters, 439, L5, 10.1086/187731

    1995 doi

  40. [49]

    1996, The Astrophysical Journal Letters, 467, L93, 10.1086/310201

    ---. 1996, The Astrophysical Journal Letters, 467, L93, 10.1086/310201

    1996 doi

  41. [50]

    K., Bellgowan, P

    Kriegeskorte, N., Simmons, W. K., Bellgowan, P. S. F., & Baker, C. I. 2009, Nature Neuroscience, 12, 535, 10.1038/nn.2303

    2009 doi

  42. [51]

    A., Mitra , D., Naidu , A., Joshi , B

    Krishnakumar , M. A., Mitra , D., Naidu , A., Joshi , B. C., & Manoharan , P. K. 2015, The Astrophysical Journal, 804, 23, 10.1088/0004-637X/804/1/23

    2015 doi

  43. [52]

    A., Manoharan , P

    Krishnakumar , M. A., Manoharan , P. K., Joshi , B. C., et al. 2021, Astronomy & Astrophysics, 651, A5, 10.1051/0004-6361/202140340

    2021 doi

  44. [53]

    G., Romano, J

    Laal, N., Lamb, W. G., Romano, J. D., et al. 2023, Phys. Rev. D, 108, 063008, 10.1103/PhysRevD.108.063008

    2023 doi

  45. [54]

    2001, Monthly Notices of the Royal Astronomical Society, 326, 274, 10.1046/j.1365-8711.2001.04606.x

    Lange, C., Camilo, F., Wex, N., et al. 2001, Monthly Notices of the Royal Astronomical Society, 326, 274, 10.1046/j.1365-8711.2001.04606.x

    2001

  46. [55]

    I., Vaughan , A

    Large , M. I., Vaughan , A. E., & Mills , B. Y. 1968, Nature, 220, 340, 10.1038/220340a0

    1968 doi

  47. [56]

    Lentati , L., Alexander , P., & Hobson , M. P. 2015, Monthly Notices of the Royal Astronomical Society, 447, 2159, 10.1093/mnras/stu2611

    2015 doi

  48. [57]

    P., et al

    Lentati , L., Alexander , P., Hobson , M. P., et al. 2014, Monthly Notices of the Royal Astronomical Society, 437, 3004, 10.1093/mnras/stt2122

    2014 doi

  49. [58]

    R., & Kramer , M

    Lorimer , D. R., & Kramer , M. 2012, Handbook of Pulsar Astronomy (Cambridge University Press)

    2012

  50. [59]

    2021, The Astrophysical Journal, 911, 45, 10.3847/1538-4357/abe62f

    Luo , J., Ransom , S., Demorest , P., et al. 2021, The Astrophysical Journal, 911, 45, 10.3847/1538-4357/abe62f

    2021 doi

  51. [60]

    N., Hobbs, G

    Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, The Astronomical Journal, 129, 1993, 10.1086/428488

    2005 doi

  52. [61]

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

    2003

  53. [62]

    M., et al

    Parthasarathy , A., Bailes , M., Shannon , R. M., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 407, 10.1093/mnras/stab037

    2021 doi

  54. [63]

    Pennucci, T. T. 2019, The Astrophysical Journal, 871, 34, 10.3847/1538-4357/aaf6ef

    2019 doi

  55. [64]

    T., Demorest , P

    Pennucci , T. T., Demorest , P. B., & Ransom , S. M. 2014, The Astrophysical Journal, 790, 93, 10.1088/0004-637X/790/2/93

    2014 doi

  56. [65]

    Perera , B. B. P., Barr , E. D., Mickaliger , M. B., et al. 2019, Monthly Notices of the Royal Astronomical Society, 487, 1025, 10.1093/mnras/stz1180

    2019 doi

  57. [66]

    Perera, B. B. P., DeCesar, M. E., Demorest, P. B., et al. 2019, Monthly Notices of the Royal Astronomical Society, 490, 4666, 10.1093/mnras/stz2857

    2019 doi

  58. [67]

    J., & Clark , C

    Pletsch , H. J., & Clark , C. J. 2015, The Astrophysical Journal, 807, 18, 10.1088/0004-637X/807/1/18

    2015 doi

  59. [68]

    R., & Lai, D

    Rafikov, R. R., & Lai, D. 2006, Physical Review D, 73, 063003, 10.1103/PhysRevD.73.063003

    2006 doi

  60. [69]

    P., Tollerud , E

    Robitaille , T. P., Tollerud , E. J., Greenfield , P., et al. 2013, Astronomy & Astrophysics, 558, A33, 10.1051/0004-6361/201322068

    2013 doi

  61. [70]

    2022, PythonCall.jl: Python and Julia in harmony

    Rowley, C. 2022, PythonCall.jl: Python and Julia in harmony. https://github.com/JuliaPy/PythonCall.jl

    2022

  62. [71]

    2022, DoubleFloats , 1.2.2

    Sarnoff, J., et al. 2022, DoubleFloats , 1.2.2. https://github.com/JuliaMath/DoubleFloats.jl

    2022

  63. [72]

    P., Joshi , B

    Singha , J., Surnis , M. P., Joshi , B. C., et al. 2021, Monthly Notices of the Royal Astronomical Society, 507, L57, 10.1093/mnrasl/slab098

    2021 doi

  64. [73]

    C., Chalumeau , A., Tiburzi , C., et al

    Susarla , S. C., Chalumeau , A., Tiburzi , C., et al. 2024, arXiv e-prints, arXiv:2409.09838, 10.48550/arXiv.2409.09838

    2024 doi arXiv

  65. [74]

    2025, Vela.jl: A Bayesian pulsar timing and noise analysis package, 0.0.7, Zenodo, 10.5281/zenodo.14609404

    Susobhanan, A. 2025, Vela.jl: A Bayesian pulsar timing and noise analysis package, 0.0.7, Zenodo, 10.5281/zenodo.14609404

    2025 doi

  66. [75]

    C., & Kumar, R

    Susobhanan, A., Gopakumar, A., Joshi, B. C., & Kumar, R. 2018, Monthly Notices of the Royal Astronomical Society, 480, 5260, 10.1093/mnras/sty2177

    2018 doi

  67. [76]

    L., Archibald, A

    Susobhanan, A., Kaplan, D. L., Archibald, A. M., et al. 2024, The Astrophysical Journal, 971, 150, 10.3847/1538-4357/ad59f7

    2024 doi

  68. [77]

    2022, Publications of the Astronomical Society of Australia, 39, e053, 10.1017/pasa.2022.46

    Tarafdar, P., Nobleson, K., Rana, P., et al. 2022, Publications of the Astronomical Society of Australia, 39, e053, 10.1017/pasa.2022.46

    2022 doi

  69. [78]

    Taylor, J. H. 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 341, 117, 10.1098/rsta.1992.0088

    1992

  70. [79]

    2015, Monthly Notices of the Royal Astronomical Society, 455, 4339, 10.1093/mnras/stv2143

    Tiburzi, C., Hobbs, G., Kerr, M., et al. 2015, Monthly Notices of the Royal Astronomical Society, 455, 4339, 10.1093/mnras/stv2143

    2015 doi

  71. [80]

    M., Bassa , C

    Tiburzi , C., Shaifullah , G. M., Bassa , C. G., et al. 2021, Astronomy & Astrophysics, 647, A84, 10.1051/0004-6361/202039846

    2021 doi

  72. [81]

    R., Simon, J., et al

    Vallisneri, M., Taylor, S. R., Simon, J., et al. 2020, The Astrophysical Journal, 893, 112, 10.3847/1538-4357/ab7b67

    2020 doi

  73. [82]

    2024, arXiv e-prints, arXiv:2412.11894, 10.48550/arXiv.2412.11894

    Valtolina , S., & van Haasteren , R. 2024, arXiv e-prints, arXiv:2412.11894, 10.48550/arXiv.2412.11894

    2024 doi arXiv

  74. [83]

    2016, Piccard: Pulsar timing data analysis package , Astrophysics Source Code Library, record ascl:1610.001

    van Haasteren , R. 2016, Piccard: Pulsar timing data analysis package , Astrophysics Source Code Library, record ascl:1610.001

    2016

  75. [84]

    2013, Monthly Notices of the Royal Astronomical Society, 428, 1147, 10.1093/mnras/sts097

    van Haasteren , R., & Levin , Y. 2013, Monthly Notices of the Royal Astronomical Society, 428, 1147, 10.1093/mnras/sts097

    2013 doi

  76. [85]

    2014, Monthly Notices of the Royal Astronomical Society, 446, 1170, 10.1093/mnras/stu2157

    van Haasteren, R., & Vallisneri, M. 2014, Monthly Notices of the Royal Astronomical Society, 446, 1170, 10.1093/mnras/stu2157

    2014 doi

  77. [86]

    J., & Vallisneri , M

    Vigeland , S. J., & Vallisneri , M. 2014, Monthly Notices of the Royal Astronomical Society, 440, 1446, 10.1093/mnras/stu312

    2014 doi

  78. [87]

    Voisin , G., Cognard , I., Freire , P. C. C., et al. 2020, Astronomy & Astrophysics, 638, A24, 10.1051/0004-6361/202038104

    2020 doi

  79. [88]

    M., & Huang , Y

    Weisberg , J. M., & Huang , Y. 2016, The Astrophysical Journal, 829, 55, 10.3847/0004-637X/829/1/55

    2016 doi

Pith tools

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