Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 82 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 18 tok/s
GPT-5 High 12 tok/s Pro
GPT-4o 96 tok/s
GPT OSS 120B 467 tok/s Pro
Kimi K2 217 tok/s Pro
2000 character limit reached

The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs (2303.15442v3)

Published 27 Mar 2023 in astro-ph.HE, astro-ph.GA, astro-ph.IM, and gr-qc

Abstract: Pulsar timing arrays (PTAs) have recently found evidence for a nanohertz-frequency stochastic gravitational-wave background (SGWB). Constraining its spectral characteristics will reveal its origins. To achieve this, we must understand how data and modeling conditions in each pulsar influence the precision and accuracy of SGWB spectral recovery, typically requiring many Bayesian analyses on real data sets and large-scale simulations that are slow and computationally taxing. To combat this, we have developed several new rapid approaches that operate on intermediate SGWB analysis products. These techniques refit SGWB spectral models to previously computed Bayesian posterior estimates of the timing power spectra. We test our new techniques on simulated PTA data sets and the NANOGrav 12.5-year data set, where in the latter our refit posterior achieves a Hellinger distance -- bounded between 0 for identical distributions and 1 for zero overlap -- from the current full production-level pipeline that is < 0.1. Our techniques are ~ $102$--$104$ times faster than the production-level likelihood and scale much more favorably (sub-linearly) as a PTA is expanded with new pulsars or observations. Our techniques also allow us to demonstrate conclusively that SGWB spectral characterization in PTA data sets is driven by the longest-timed pulsars and the best-measured power spectral densities. Indeed, the common-process spectral properties found in the NANOGrav 12.5-year data set are given by analyzing only the ~14 longest-timed pulsars out of the full 45 pulsar array, and we find that the 'shallowing' of the common-process power-law model occurs when gravitational-wave frequencies higher than ~50 nanohertz are included. The implementation of our techniques is openly available as a software suite to allow fast and flexible PTA SGWB spectral characterization and model selection.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (41)
  1. R. S. Foster and D. C. Backer, Constructing a Pulsar Timing Array, ApJ 361, 300 (1990).
  2. R. Hellings and G. Downs, Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, The Astrophysical Journal 265, L39 (1983).
  3. E. S. Phinney, A practical theorem on gravitational wave backgrounds (2001).
  4. A. Sesana, Insights into the astrophysics of supermassive black hole binaries from pulsar timing observations, Classical and Quantum Gravity 30, 224014 (2013).
  5. L. Sampson, N. J. Cornish, and S. T. McWilliams, Constraining the solution to the last parsec problem with pulsar timing, Physical Review D 91, 084055 (2015).
  6. S. R. Taylor, J. Simon, and L. Sampson, Constraints on the dynamical environments of supermassive black-hole binaries using pulsar-timing arrays, Physical Review Letters 118, 181102 (2017).
  7. A. Sesana, A. Vecchio, and C. N. Colacino, The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays, Monthly Notices of the Royal Astronomical Society 390, 192 (2008), https://academic.oup.com/mnras/article-pdf/390/1/192/2959688/mnras0390-0192.pdf .
  8. T. W. B. Kibble, Topology of Cosmic Domains and Strings, Journal of Physics A  (1976).
  9. P. Schwaller, Gravitational waves from a dark phase transition, Physical Review Letters 115, 181101 (2015).
  10. R. van Haasteren and M. Vallisneri, New advances in the gaussian-process approach to pulsar-timing data analysis, Physical Review D 90, 104012 (2014).
  11. R. van Haasteren and M. Vallisneri, Low-rank approximations for large stationary covariance matrices, as used in the bayesian and generalized-least-squares analysis of pulsar-timing data, Monthly Notices of the Royal Astronomical Society 446, 1170 (2015).
  12. J. Cordes and R. Shannon, A measurement model for precision pulsar timing, arXiv preprint arXiv:1010.3785  (2010).
  13. S. R. Taylor, J. R. Gair, and L. Lentati, Weighing the evidence for a gravitational-wave background in the first international pulsar timing array data challenge, Phys. Rev. D 87, 044035 (2013).
  14. W. Ratzinger and P. Schwaller, Whispers from the dark side: Confronting light new physics with NANOGrav data, SciPost Physics 10, 10.21468/scipostphys.10.2.047 (2021).
  15. D. Wang, Novel physics with international pulsar timing array: Axionlike particles, domain walls and cosmic strings (2022).
  16. D. W. Scott, On optimal and data-based histograms, Biometrika 66, 605 (1979), https://academic.oup.com/biomet/article-pdf/66/3/605/632347/66-3-605.pdf .
  17. D. Freedman and P. Diaconis, On the histogram as a density estimator: L 2 theory, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 57, 453 (1981).
  18. E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics 33, 1065 (1962).
  19. M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics 27, 832 (1956).
  20. V. A. Epanechnikov, Non-parametric estimation of a multivariate probability density, Theory of Probability & Its Applications 14, 153 (1969), https://doi.org/10.1137/1114019 .
  21. S. J. Sheather and M. C. Jones, A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society. Series B (Methodological) 53, 683 (1991).
  22. E. D. Hellinger, Journal für die reine und angewandte mathematik,   (1909).
  23. P. A. Rosado, A. Sesana, and J. Gair, Expected properties of the first gravitational wave signal detected with pulsar timing arrays, Monthly Notices of the Royal Astronomical Society 451, 2417 (2015).
  24. K. Pearson, Vii. note on regression and inheritance in the case of two parents, proceedings of the royal society of London 58, 240 (1895).
  25. G. Ashton and C. Talbot, Bilby-mcmc: an mcmc sampler for gravitational-wave inference, Monthly Notices of the Royal Astronomical Society 507, 2037 (2021).
  26. R. E. Kass and A. E. Raftery, Bayes factors, Journal of the american statistical association 90, 773 (1995).
  27. J. M. Dickey, The weighted likelihood ratio, linear hypotheses on normal location parameters, The Annals of Mathematical Statistics , 204 (1971).
  28. B. P. Carlin and S. Chib, Bayesian model choice via markov chain monte carlo methods, Journal of the Royal Statistical Society: Series B (Methodological) 57, 473 (1995).
  29. S. J. Godsill, On the relationship between markov chain monte carlo methods for model uncertainty, Journal of computational and graphical statistics 10, 230 (2001).
  30. J. Skilling, Nested sampling, in Aip conference proceedings, Vol. 735 (American Institute of Physics, 2004) pp. 395–405.
  31. J. Buchner, Nested sampling methods, Statistic Surveys 17, 169 (2023).
  32. J. Buchner, UltraNest - a robust, general purpose Bayesian inference engine, The Journal of Open Source Software 6, 3001 (2021), arXiv:2101.09604 [stat.CO] .
  33. C. J. Moore, S. R. Taylor, and J. R. Gair, Estimating the sensitivity of pulsar timing arrays, Classical and Quantum Gravity 32, 055004 (2015).
  34. J. S. Hazboun, J. D. Romano, and T. L. Smith, Realistic sensitivity curves for pulsar timing arrays, Phys. Rev. D 100, 104028 (2019).
  35. N. J. Cornish and L. Sampson, Towards robust gravitational wave detection with pulsar timing arrays, Physical Review D 93, 104047 (2016).
  36. D. Rezende and S. Mohamed, Variational inference with normalizing flows, in International conference on machine learning (PMLR, 2015) pp. 1530–1538.
  37. J. Ellis and R. van Haasteren, jellis18/ptmcmcsampler: Official release (2017).
  38. R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2018).
  39. T. Odland, tommyod/kdepy: Kernel density estimation in python (2018).
  40. S. R. Hinton, ChainConsumer, The Journal of Open Source Software 1, 00045 (2016).
  41. M. Vallisneri, libstempo: Python wrapper for Tempo2, Astrophysics Source Code Library, record ascl:2002.017 (2020), ascl:2002.017 .
Citations (36)
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Summary

We haven't generated a summary for this paper yet.

Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.