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arxiv: 2603.06010 · v2 · submitted 2026-03-06 · 🌀 gr-qc · astro-ph.IM

Recognition: no theorem link

Accelerated Time-domain Analysis for Gravitational Wave Astronomy

Vaishak Prasad
Authors on Pith no claims yet

Pith reviewed 2026-05-15 15:39 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.IM
keywords gravitational wavestime-domain analysislikelihood evaluationparameter estimationGPU accelerationstructured linear algebranoise covariancegravitational wave astronomy
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The pith

A fully time-domain formulation makes gravitational-wave likelihood evaluation practical at scale without frequency-domain approximations.

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

Standard gravitational-wave pipelines approximate detector noise as stationary to enable fast frequency-domain inner products via Fourier transforms. This paper instead builds an end-to-end inference method that stays entirely in the time domain, computing the Gaussian likelihood directly from the noise covariance. Structured linear algebra together with software and hardware acceleration renders the computation efficient enough for realistic data volumes. The resulting implementation handles gaps, sharp boundaries, and disjoint segments while supporting GPU execution. Injection tests confirm that the time-domain results match conventional methods and deliver measurable speedups.

Core claim

We develop a self-contained, end-to-end, fully time-domain formulation of gravitational-wave inference and present an implementation that makes the likelihood evaluation practical at scale by exploiting structured linear algebra, software, and hardware acceleration. We validate the method using injections and demonstrate speedups for likelihood evaluation on modern GPUs. We present tdanalysis, an accelerated implementation that handles gaps, sharp boundaries, and multiple disjoint segments, and supports GPUs.

What carries the argument

The time-domain Gaussian likelihood, evaluated via structured linear algebra on the noise covariance matrix to avoid the circulant Fourier approximation.

If this is right

  • The method works directly with gapped or segmented data without extra windowing or approximation steps.
  • Likelihood evaluations run faster on modern GPUs than the conventional frequency-domain route.
  • The same framework supports both search and parameter-estimation tasks in gravitational-wave astronomy.
  • Realistic, non-stationary noise covariances can be used without forcing a circulant structure.

Where Pith is reading between the lines

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

  • The approach may prove useful for analyzing short signals or those overlapping detector transients where stationarity assumptions break down.
  • Hardware acceleration could enable low-latency pipelines that respond in seconds rather than minutes.
  • The time-domain structure opens a route to incorporating non-Gaussian or non-stationary noise models without reformulating the inner product.
  • Hybrid codes that switch between time and frequency domains for different parts of the same analysis become feasible.

Load-bearing premise

Structured linear algebra can evaluate the full time-domain likelihood at scale without numerical instabilities or accuracy loss relative to the frequency-domain circulant method.

What would settle it

A direct numerical comparison of likelihood values and recovered posteriors between the new time-domain code and standard frequency-domain code on identical injection data sets, checking agreement to within expected numerical precision.

Figures

Figures reproduced from arXiv: 2603.06010 by Vaishak Prasad.

Figure 1
Figure 1. Figure 1: FIG. 1. Average amount of CPU FLOPs for 32-bit arithmetic and the memory bandwidth since 1990 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The estimated autocorrelation and PSD around the GW250114 event in the Hanford detector. The left panel shows [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Caption [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: We do not benchmark the lower-triangular solve method because likelihood computation times are un￾predictable in this approach. The GPU benchmarks are shown as single likelihood evaluation times in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Benchmark results for direct Cholesky decomposed whitening operator method, and the GSCE method. The left plot [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Injection recovery from the GPU run. This corner plot shows some of the parameters from an 11-dimensional PE run [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: 2. Gaussian noise injection We repeat the analysis from the zero-noise case while also injecting noise into the detector. The noise draw, consistent with the estimated noise covariance matrix, was computed by drawing Nsam points ˜n from the stan￾dard normal distribution and then applying the inverse whitening filter, i.e., Ln˜. The results of the analysis are shown in the second row of [PITH_FULL_IMAGE:fi… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The recovered maximum Likelihood waveform. The top panel of the left plot shows the maximum-likelihood waveform [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Marginal distributions from GW250114 PE analysis. Here, we show the 1D marginal distributions of mass ratio (left), [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The recovered maximum Likelihood waveforms. The left panels show whitened (decorrelated and standardized) data [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Matched filter SNR distributions. Here, the pos [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Recovery of parameters from a ringdown injection study. This corner plot shows the one, two, and three sigma [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
read the original abstract

Most current compact-binary searches and parameter-estimation pipelines evaluate the Gaussian-noise likelihood approximately using frequency-domain inner products with great success in analyzing gravitational-wave signals. This is historically motivated by (i) the approximate stationarity of detector noise on sufficiently long timescales, allowing a circulant approximation in the domain that diagonalizes the noise covariance in the Fourier basis, and (ii) the efficiency of matched filtering via fast Fourier transforms. However, the advantage of frequency-domain analysis comes with its own limitations. In this article, we develop a self-contained, end-to-end, \emph{fully time-domain} formulation of gravitational-wave inference and present an implementation that makes the likelihood evaluation practical at scale by exploiting structured linear algebra, software, and hardware acceleration. We validate the method using injections and demonstrate speedups for likelihood evaluation and on modern GPUs. We present \emph{tdanalysis}, an accelerated implementation that handles gaps, sharp boundaries, and multiple disjoint segments, and supports GPUs. We demonstrate some of its applications in gravitational wave astronomy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a fully time-domain formulation of the Gaussian-noise likelihood for gravitational-wave inference on compact binary signals. It replaces the conventional frequency-domain circulant approximation with structured linear algebra operations on the time-domain covariance matrix, enabling direct handling of gaps, sharp boundaries, and multiple disjoint segments. An implementation named tdanalysis is presented that exploits software optimizations and GPU hardware to make likelihood evaluations practical at scale, with validation performed via signal injections and reported speedups.

Significance. If the time-domain formulation preserves numerical accuracy and conditioning equivalent to frequency-domain methods for realistic, non-stationary detector noise, the work would enable more flexible analyses of gapped or non-stationary data segments without uncontrolled approximations. The GPU-accelerated implementation could also support scaling to higher-dimensional parameter spaces or real-time applications, addressing a practical bottleneck in current pipelines.

major comments (2)
  1. [Abstract] Abstract: the validation statement ('validated the method using injections') provides no quantitative metrics such as recovered SNR bias, parameter posterior width ratios, or direct likelihood-value comparisons against the frequency-domain circulant baseline once gaps and windowing are introduced; without these, it is impossible to confirm that the structured-algebra quadratic form and log-determinant remain free of accuracy loss.
  2. [Implementation and validation sections] The central claim that structured linear algebra (e.g., fast solvers for block-Toeplitz or low-rank-updated covariances) evaluates the time-domain likelihood 'without introducing numerical instabilities' is load-bearing yet unsupported by explicit conditioning numbers, residual norms, or floating-point error budgets for realistic PSD-derived covariances; this must be demonstrated before the 'no accuracy loss' assertion can be accepted.
minor comments (2)
  1. [Methods] Notation for the time-domain covariance matrix and its factorization should be introduced with an explicit equation early in the text to aid readability.
  2. [Results] Figure captions for the injection-recovery plots should include the exact noise realization parameters and gap locations used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive suggestions. We agree that strengthening the quantitative validation will improve the manuscript and have revised the abstract and validation sections accordingly. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the validation statement ('validated the method using injections') provides no quantitative metrics such as recovered SNR bias, parameter posterior width ratios, or direct likelihood-value comparisons against the frequency-domain circulant baseline once gaps and windowing are introduced; without these, it is impossible to confirm that the structured-algebra quadratic form and log-determinant remain free of accuracy loss.

    Authors: We agree that the original abstract was insufficiently quantitative. In the revised manuscript we have expanded the abstract to report explicit metrics from the injection campaign: recovered SNR bias remains below 0.05 sigma across the tested population, posterior width ratios relative to the frequency-domain baseline stay within 3-7 percent, and direct likelihood-value differences for gapped segments are at the level of 10^{-4} in log-likelihood units. These numbers are now stated in the abstract and supported by the new Table 1 in the validation section. revision: yes

  2. Referee: [Implementation and validation sections] The central claim that structured linear algebra (e.g., fast solvers for block-Toeplitz or low-rank-updated covariances) evaluates the time-domain likelihood 'without introducing numerical instabilities' is load-bearing yet unsupported by explicit conditioning numbers, residual norms, or floating-point error budgets for realistic PSD-derived covariances; this must be demonstrated before the 'no accuracy loss' assertion can be accepted.

    Authors: We accept that the original text lacked the requested numerical diagnostics. The revised validation section now includes: (i) condition numbers of the time-domain covariance matrices (typically 10^7 to 10^9 for realistic LIGO PSDs over 4-second segments), (ii) residual norms of the Cholesky and low-rank-update solvers (consistently below 10^{-12} in double precision), and (iii) a floating-point error budget showing that the time-domain quadratic form and log-determinant agree with the frequency-domain circulant result to within 10^{-10} relative error even after gap insertion and windowing. These diagnostics are presented in a new subsection and confirm that no accuracy loss is introduced beyond standard floating-point limits. revision: yes

Circularity Check

0 steps flagged

Direct algebraic rewrite of Gaussian likelihood in time domain with no reduction to inputs

full rationale

The paper formulates the time-domain likelihood as an explicit rewrite of the standard Gaussian noise model using the covariance matrix directly in the time domain, then accelerates it via structured linear algebra (block-Toeplitz solvers, GPU Cholesky, handling of gaps). No equation is shown to equal a fitted parameter or prior result by construction; the central claim is that this structured evaluation matches the frequency-domain result to within numerical tolerance, which is checked via injection studies rather than assumed. No self-citation chain or ansatz smuggling appears in the load-bearing steps. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Gaussian-noise likelihood being exactly equivalent when expressed in the time domain and on the assumption that structured linear algebra can make its evaluation computationally competitive.

axioms (1)
  • domain assumption Detector noise is Gaussian with a known covariance matrix that can be handled directly in the time domain.
    This is the foundational assumption of the likelihood used in current GW pipelines, now applied without the circulant Fourier approximation.

pith-pipeline@v0.9.0 · 5466 in / 1222 out tokens · 31050 ms · 2026-05-15T15:39:05.367463+00:00 · methodology

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Reference graph

Works this paper leans on

162 extracted references · 162 canonical work pages · 29 internal anchors

  1. [1]

    or by compromising information at the boundaries. In what follows, we relax the circulant assumption and remain in the time domain, thereby removing the need for tapering or windowing and enabling analysis of sharply terminated segments of the signal that start and/or end abruptly. 5 FIG. 2. Thetdanalysisinfrastructure for time domain analy- sis. This cla...

    work page

  2. [2]

    This is anO(N) operation, both in terms of computational complexity and memory traffic

    Data projection and conditioning Once the polarizations (h+,x) and the antenna patterns fp,x of the detectors are generated, the polarizations are projected onto the detector frame by computing the dot producth +f++hxfx. This is anO(N) operation, both in terms of computational complexity and memory traffic. Conditioning the waveform in the time domain inv...

    work page

  3. [3]

    II, one can factorize the covari- ance matrix using Cholesky decompositionC=L ⊤L, endowing the analysis with a whitening operator

    Factorization of the Covariance matrix As discussed in Sec. II, one can factorize the covari- ance matrix using Cholesky decompositionC=L ⊤L, endowing the analysis with a whitening operator. This operation needs to be done once, and for a denseC, the complexity isO(N 3); for Toeplitz/banded matrices, some implementations reduce this toO(N 2). Either way, ...

    work page

  4. [4]

    This corresponds toN= 16384

    Memory bandwidth Consider analyzing a signal that is 4slong, sampled at 4096Hz. This corresponds toN= 16384. Given the sen- sitivities of the current generation of detectors, FP32 is sufficient to avoid numerical underflow/overflow in vari- ous matrix operations during likelihood evaluation, given the inverse covariance or the whitening matrix. This means...

    work page 2005

  5. [5]

    With AVX, Single Instruction Multiple Data (SIMD) means that processors are no longer restricted to execute a single floating-point instruction at a time

    CPU acceleration Various improvements in CPU instruction architec- tures, including Advanced Vector Extensions (AVX) [117–119], Fused Multiply-Add (FMA) [116, 120, 121], and increased core counts, and their use via directives such as OpenMP [126, 127] and POSIX/Pthread [128, 129], have greatly enhanced CPU vector capabilities. With AVX, Single Instruction...

    work page

  6. [6]

    Their architecture, composed of hundreds and thousands of streaming multiprocessors, is perfect for op- erating on large matrices

    GPU acceleration General Purpose Graphics Processing Units are a pow- erhouse for linear algebra, exploiting the Single Instruc- tion Multiple Threads (SIMT) nature of linear algebra routines. Their architecture, composed of hundreds and thousands of streaming multiprocessors, is perfect for op- erating on large matrices. Modern GPUs can have a throughput...

    work page

  7. [7]

    We find that ensuring all vectors and matrices are contiguous in memory, and in Fortran ordering, can yield up upto 2x speedups, which we implement

    Memory ordering In Python, vectors and matrices are not guaranteed to be contiguous in memory. We find that ensuring all vectors and matrices are contiguous in memory, and in Fortran ordering, can yield up upto 2x speedups, which we implement. 11

    work page

  8. [8]

    When offloading linear alge- bra or inner-product computations to GPUs using the ‘CDO‘ method, there are multiple Application Program- ming Interface (API) options

    Code optimization Most of the other software speedups we implement are relevant to GPUs. When offloading linear alge- bra or inner-product computations to GPUs using the ‘CDO‘ method, there are multiple Application Program- ming Interface (API) options. The most common and generic software API for this is TensorFlow [138] or Py- Torch [139]. The other opt...

    work page

  9. [9]

    Given that FP32 has a dynamic range of 10 ±38, it is possible to carry out all the analysis with FP32 with appropriate normalization

    Precision We note that the autocorrelation function generally has a dynamic floating-point range of 10 −42 to 10 −34, i.e., spanning about 8 orders of magnitude (see Fig 3). Given that FP32 has a dynamic range of 10 ±38, it is possible to carry out all the analysis with FP32 with appropriate normalization. However, the necessary ma- trices and whitening o...

    work page

  10. [10]

    When using a multiprocessing pool, the average number of likelihood calls per second is approximately 10 times slower

    Single likelihood evaluation times on CPUs are about 3-15 times slower than frequency domain when directly using the ‘CDO’ method. When using a multiprocessing pool, the average number of likelihood calls per second is approximately 10 times slower

    work page

  11. [11]

    How- ever, they are still 1-5x slower than the FD method

    On GPUs, the ‘CDO’ method attains about 2-10x speedup per likelihood evaluation over CPUs. How- ever, they are still 1-5x slower than the FD method. Using data center GPUs capable of FP64 compute and optimizing custom GPU kernels with HIP can match CPU FD valuation times

    work page

  12. [12]

    Implementing and benchmarking this method, we find that the GSCE method is approximately only slower than the FD method by a factor of∼2

    When using ‘GSCE’ on CPUs, the likelihood eval- uation times and the average number of likelihood calls in a given duration across the multiprocess- ing pools are approximately the same as in the FD approach when using this method. Implementing and benchmarking this method, we find that the GSCE method is approximately only slower than the FD method by a ...

    work page

  13. [13]

    The effective speedup is thus≈ 10×n pool, wheren pool is the pool size for proposals

    On CPUs, the ‘GSCE’ method is roughly 10 times faster than the ‘CDO’ method, while at the same time not using as much memory bandwidth as the ‘CDO’ method, leaving room for process-based parallelization. The effective speedup is thus≈ 10×n pool, wheren pool is the pool size for proposals

    work page

  14. [14]

    Thus, we recommend using a multiprocess- ing pool size equal to the number of physical cores available to achieve the best results

    We find that using process-based parallelism is more advantageous than shared-memory paral- lelism. Thus, we recommend using a multiprocess- ing pool size equal to the number of physical cores available to achieve the best results. B. Parameter estimation In this section, we demonstrate the PE results obtained bytdanalysisusing a GW250114-like and GW23081...

    work page

  15. [15]

    We run the CDO method, fixing 4 of the 11 parameters, viz.r a, δ, tc, θjN

    Zero noise injection First, we inject a complete GW230814-like signal into the detector with zero noise and analyze it with NR- Sur7dq4, the waveform of choice for all the runs pre- sented here. We run the CDO method, fixing 4 of the 11 parameters, viz.r a, δ, tc, θjN . The corner plot from some of the 11d parameters is shown in Fig. 6. The run took about...

    work page

  16. [16]

    Gaussian noise injection We repeat the analysis from the zero-noise case while also injecting noise into the detector. The noise draw, consistent with the estimated noise covariance matrix, was computed by drawingN sam points˜ nfrom the stan- dard normal distribution and then applying the inverse whitening filter, i.e.,L˜n. The results of the analysis are...

    work page 2000

  17. [17]

    Real data We analyze the real data with detector noise for GW250114. We carry out three separate analyses, in- volving (i) the full IMR signal, (ii) the inspiral-only por- tion truncated at−200Mbefore merger, and (iii) the ringdown portion 10Mafter the peak of the signal. In Fig.??. The set of all reconstructed posterior waveforms is shown in the top and ...

    work page

  18. [18]

    B. P. e. a. Abbott (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. X9, 031040 (2019)

    work page 2019

  19. [19]

    B. P. Abbottet al., Gwtc-2.1: Deep extended catalog of compact binary coalescences observed by ligo and virgo during the first half of the third observing run (2021), arXiv:2108.01045 [gr-qc]

    work page arXiv 2021

  20. [20]

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

    R. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration), Phys. Rev. X13, 041039 (2023), arXiv:2111.03606 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  21. [21]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), arXiv:2508.18080 [gr-qc] (2025), submitted for publica- tion to ApJ Lett

    work page arXiv 2025

  22. [22]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), arXiv:2508.18083 [astro-ph.HE] (2025), submitted for publication to ApJ Lett

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  23. [23]

    B. P. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), Physical Review D100, 104036 (2019)

    work page 2019

  24. [24]

    Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), Physical Review D103, 122002 (2021)

    R. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), Physical Review D103, 122002 (2021)

    work page 2021

  25. [25]

    Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration), Phys- ical Review D112, 084080 (2025)

    R. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration), Phys- ical Review D112, 084080 (2025)

    work page 2025

  26. [26]

    A. G. Abacet al.(LIGO Scientific, Virgo, KAGRA), Phys. Rev. Lett.135, 111403 (2025), arXiv:2509.08054 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  27. [27]

    LIGO-Virgo-KAGRA Collaboration (LIGO Scientific, 19 VIRGO, KAGRA), arXiv:2509.08099 [gr-qc] (2025), https://arxiv.org/abs/2509.08099

    work page internal anchor Pith review arXiv 2025

  28. [28]

    The LIGO Scientific Collaboration, Classical and Quan- tum Gravity32, 074001 (2015)

    work page 2015

  29. [29]

    Advanced Virgo: a 2nd generation interferometric gravitational wave detector

    F. Acernese, M. Agathos, K. Agatsuma, D. Aisa, N. Allemandou, A. Allocca, J. Amarni, P. Astone, G. Balestri, G. Ballardin, and et al., Classical and Quan- tum Gravity32, 024001 (2015), arXiv:1408.3978 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  30. [30]

    Somiya, Classical and Quantum Gravity29, 124007 (2012), arXiv:1111.7185 [gr-qc]

    K. Somiya, Classical and Quantum Gravity29, 124007 (2012), arXiv:1111.7185 [gr-qc]

    work page arXiv 2012

  31. [32]

    Analysis Framework for the Prompt Discovery of Compact Binary Mergers in Gravitational-wave Data

    C. Messick, K. Blackburn, P. Brady, P. Brockill, K. Cannon, R. Cariou, S. Caudill, D. Chatterjee, J. D. E. Creighton, S. Fairhurst, H. Gabbard, P. God- win, C. Hanna, D. Keppel, G. Lovelace, D. Meacher, A. Pace, P. Patel, S. Privitera, K. Riles, L. Singer, R. Spero, J. Staff, K. Ueno, A. Viets, L. Wade, and A. R. Williamson, Physical Review D95, 042001 (2...

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [33]

    Cannon, S

    K. Cannon, S. Caudill, C.-Y. Chan, B. Cousins, J. D. E. Creighton, B. Ewing, H. Fong, P. Godwin, C. Hanna, S. Hooper, R. Huxford, R. Magee, D. Meacher, C. Mes- sick, S. Morisaki, D. Mukherjee, H. Ohta, A. Pace, S. Privitera, I. de Ruiter, S. Sachdev, L. Singer, D. Singh, R. Tapia, L. Tsukada, D. Tsuna, T. Tsutsui, K. Ueno, A. Viets, L. Wade, and M. Wade, ...

    work page 2021

  33. [34]

    Babak, R

    S. Babak, R. Biswas, P. R. Brady, D. A. Brown, K. Can- non, G. Carapella, S. Caudill, V. Raymond, and others, Physical Review D87, 024033 (2013)

    work page 2013

  34. [35]

    Aubin, F

    F. Aubin, F. Brighenti, R. Chierici, D. Estevez, G. Greco, G. M. Guidi, V. Juste, F. Marion, B. Mours, E. Nitoglia, O. Sauter, and V. Sordini, Classical and Quantum Gravity38, 095004 (2021), arXiv:2012.11512 [astro-ph.IM]

    work page arXiv 2021

  35. [36]

    Q. Chu, M. Kovalam, L. Wen, T. Slaven-Blair, J. Bosveld, Y. Chen, P. Clearwater, A. Codoreanu, Z. Du, X. Guo, X. Guo, K. Kim, T. G. F. Li, V. Oloworaran, F. Panther, J. Powell, A. S. Sengupta, K. Wette, and X. Zhu, Physical Review D105, 024023 (2022), arXiv:2011.06787 [gr-qc]

    work page arXiv 2022

  36. [37]

    Method for detection and reconstruction of gravitational wave transients with networks of advanced detectors

    S. Klimenko, G. Vedovato, M. Drago, F. Salemi, V. Ti- wari, G. A. Prodi, C. Lazzaro, K. Ackley, S. Tiwari, C. F. da Silva, and G. Mitselmakher, Physical Review D93, 042004 (2016), arXiv:1511.05999 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [38]

    Drago, V

    M. Drago, V. Gayathri, S. Klimenko, C. Lazzaro, E. Milotti, G. Mitselmakher, V. Necula, B. O’Brian, G. A. Prodi, F. Salemi, M. Szczepanczyk, S. Tiwari, V. Tiwari, G. Vedovato, and I. Yakushin, SoftwareX14, 100678 (2021), arXiv:2006.12604 [gr-qc]

    work page arXiv 2021

  38. [39]

    Robinet, N

    F. Robinet, N. Arnaud, N. Leroy, D. Macleod, and J. McIver, SoftwareX12, 100620 (2020), arXiv:2007.11374 [astro-ph.IM]

    work page arXiv 2020

  39. [40]

    LIGO Scientific Collaboration and Virgo Collaboration, Physical Review D93, 122003 (2016), arXiv:1602.03839 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  40. [41]

    Wiener, Acta Mathematica55, 117 (1930)

    N. Wiener, Acta Mathematica55, 117 (1930)

    work page 1930

  41. [42]

    Khintchine, Mathematische Annalen109, 604 (1934)

    A. Khintchine, Mathematische Annalen109, 604 (1934)

    work page 1934

  42. [43]

    Schuster, Terrestrial Magnetism3, 13 (1898)

    A. Schuster, Terrestrial Magnetism3, 13 (1898)

    work page

  43. [44]

    M. S. Bartlett, Biometrika37, 1 (1950)

    work page 1950

  44. [45]

    R. B. Blackman and J. W. Tukey, Bell System Technical Journal (1958)

    work page 1958

  45. [46]

    J. W. Cooley and J. W. Tukey, Mathematics of Com- putation19, 297 (1965)

    work page 1965

  46. [48]

    Whittle, Journal of the Royal Statistical Society: Se- ries B (Methodological)15, 125 (1953)

    P. Whittle, Journal of the Royal Statistical Society: Se- ries B (Methodological)15, 125 (1953)

    work page 1953

  47. [49]

    Sathyaprakash and S

    B. Sathyaprakash and S. Dhurandhar, Phys. Rev. D44, 3819 (1991)

    work page 1991

  48. [50]

    Dhurandhar and B

    S. Dhurandhar and B. Sathyaprakash, Phys. Rev. D49, 1707 (1994)

    work page 1994

  49. [51]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Class. Quant. Grav.37, 055002 (2020), arXiv:1908.11170 [gr- qc]

    work page arXiv 2020

  50. [52]

    Detection, Measurement and Gravitational Radiation

    L. Finn, Phys. Rev. D46, 5236 (1992), gr-qc/9209010

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  51. [53]

    Observing binary inspiral in gravitational radiation: One interferometer

    L. Finn and D. Chernoff, Phys. Rev. D47, 2198 (1993), gr-qc/9301003

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  52. [54]

    Christensen and R

    N. Christensen and R. Meyer, Phys. Rev. D58, 082001 (1998)

    work page 1998

  53. [55]

    Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data

    N. Christensen and R. Meyer, Physical Review D64, 022001 (2001), arXiv:gr-qc/0102018

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  54. [56]

    Evolution of Binary Black Hole Spacetimes

    F. Pretorius, Phys. Rev. Lett.95, 121101 (2005), arXiv:gr-qc/0507014

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  55. [57]

    Campanelli, C

    M. Campanelli, C. Lousto, P. Marronetti, and Y. Zlo- chower, Phys. Rev. Lett.96, 111101 (2006), arXiv:gr- qc/0511048

    work page arXiv 2006

  56. [58]

    Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

    C. Cutler and E. E. Flanagan, Phys. Rev. D49, 2658 (1994), arXiv:gr-qc/9402014

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  57. [59]

    Effective one-body approach to general relativistic two-body dynamics

    A. Buonanno and T. Damour, Phys. Rev.D59, 084006 (1999), arXiv:gr-qc/9811091 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  58. [60]

    Effective-one-body model for black-hole binaries with generic mass ratios and spins

    A. Taracchiniet al., Phys. Rev. D89, 061502 (2014), arXiv:1311.2544 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  59. [61]

    Phenomenological template family for black-hole coalescence waveforms

    P. Ajithet al., Class. Quantum Grav.24, S689 (2007), arXiv:0704.3764 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  60. [62]

    S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, and M. Tiglio, Phys. Rev. X4, 031006 (2014), arXiv:1308.3565 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  61. [63]

    L. S. Finn, Phys. Rev. D46, 5236 (1992), arXiv:gr- qc/9209010

    work page arXiv 1992

  62. [64]

    Symplectic analog of Calabi's conjecture for Calabi--Yau threefolds

    P. Jaranowski and A. Kr´ olak, arXiv:1203.2665 [gr-qc] (2012),https://arxiv.org/abs/1203.2665

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  63. [65]

    Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library

    J. Veitch, V. Raymond, B. Farr, W. Farr, P. Graff, S. Vitale, B. Aylott, K. Blackburn, N. Christensen, M. Coughlin,et al., Phys. Rev. D91, 042003 (2015), arXiv:1409.7215

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  64. [66]

    S. A. Usmanet al., arXiv:1508.02357 [gr-qc] (2015), https://arxiv.org/abs/1508.02357

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  65. [67]

    Ashton, M

    G. Ashton, M. H¨ ubner, P. D. Lasky, C. Talbot, K. Ack- ley, S. Biscoveanu, Q. Chu, A. Divakarla, P. J. Easter, B. Goncharov,et al., Astrophys. J. Suppl. Ser.241, 27 (2019). 20

    work page 2019

  66. [68]

    P. D. Welch, IEEE Transactions on Audio and Electroa- coustics15, 70 (1967)

    work page 1967

  67. [69]

    N. J. Cornish, T. B. Littenberg, B. B´ ecsy, K. Chatzi- ioannou, J. A. Clark, S. Ghonge, and M. Mill- house, Physical Review D103, 044006 (2021), arXiv:2011.09494 [gr-qc]

    work page arXiv 2021

  68. [70]

    G. L. Turin, IRE Transactions on Information Theory 6, 311 (1960)

    work page 1960

  69. [71]

    C. W. Helstrom,Statistical Theory of Signal Detection, 2nd ed. (Pergamon Press, 1968)

    work page 1968

  70. [72]

    L. A. Wainstein and V. D. Zubakov,Extraction of Sig- nals from Noise(Dover Publications, 1970)

    work page 1970

  71. [73]

    Matched filtering of gravitational waves from inspiraling compact binaries: Computational cost and template placement

    B. Owen and B. Sathyaprakash, Phys. Rev. D60, 022002 (1999), arXiv:gr-qc/9808076

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  72. [74]

    Metropolis, A

    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, The Journal of Chemical Physics21, 1087 (1953)

    work page 1953

  73. [75]

    W. K. Hastings, Biometrika57, 97 (1970)

    work page 1970

  74. [76]

    C. J. Geyer, inComputing Science and Statistics: Pro- ceedings of the 23rd Symposium on the Interface(Fair- fax Station, VA, 1991) pp. 156–163

    work page 1991

  75. [77]

    R. H. Swendsen and J.-S. Wang, Physical Review Let- ters57, 2607 (1986)

    work page 1986

  76. [78]

    Hukushima and K

    K. Hukushima and K. Nemoto, Journal of the Physical Society of Japan65, 1604 (1996)

    work page 1996

  77. [79]

    Marinari and G

    E. Marinari and G. Parisi, Europhysics Letters19, 451 (1992)

    work page 1992

  78. [80]

    R. M. Neal, Statistics and Computing6, 353 (1996)

    work page 1996

  79. [81]

    P. J. Green, Biometrika82, 711 (1995)

    work page 1995

  80. [82]

    Siegert pseudostates: completeness and time evolution

    J. Skilling, inBayesian Inference and Maximum En- tropy Methods in Science and Engineering, AIP Con- ference Proceedings, Vol. 735 (2004) pp. 395–405, arXiv:physics/0408051

    work page internal anchor Pith review Pith/arXiv arXiv 2004

Showing first 80 references.