Adaptive kernel density estimation proposal in gravitational wave data analysis

Falxa, M.; Babak, S.; Jeune, M. Le

doi:10.1103/physrevd.107.022008

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…Bayesian evidence was used for model selection, where the Bayes factor for one hypothesis over the other is equal to the ratio of the two evidence values corresponding to these hypotheses. The posterior evaluation was done mainly with PTMCMCSAMPLER with other samplers used for cross-checking: m3c2 (Falxa et al 2023), Eryn (Karnesis et al 2023), and (Williams et al 2021).…”

Section: Parametermentioning

confidence: 99%

The second data release from the European Pulsar Timing Array

Antoniadis¹,

Babak²,

Nielsen³

et al. 2023

A&A

442

106

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We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). A robust GWB detection is conditioned upon resolving the Hellings-Downs angular pattern in the pairwise crosscorrelation of the pulsar timing residuals. Additionally, the GWB is expected to yield the same (common) spectrum of temporal correlations across pulsars, which is used as a null hypothesis in the GWB search. Such a common-spectrum process has already been observed in pulsar timing data. We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of 4%. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of 60 and a false alarm probability of about 0.1% (≳ 3σ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The latest EPTA data from new generation observing systems show non-negligible evidence for the GWB. At the same time, the inferred spectrum is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of (2.5 ± 0.7) × 10 −15 at a reference frequency of 1 yr −1 . Further investigation of these issues is required for reliable astrophysical interpretations of this signal. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.

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Section: Parametermentioning

confidence: 99%

The second data release from the European Pulsar Timing Array

Antoniadis¹,

Babak²,

Nielsen³

et al. 2023

A&A

442

106

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“…Therefore, reconstructing phase space structures from measurements is highly desirable as it provides critical information about the behavior and trends of individual beams in phase space. This paper presents a model of the beam core in phase space and demonstrates how kernel density estimation can be used to interpolate experimental data and reconstruct the phase space structure as a continuous function [9]. This approach offers a powerful tool for analyzing beam dynamics and could have important applications in areas such as particle accelerators and ion implantation [10].…”

Section: Introductionmentioning

confidence: 99%

Modeling of the beam core in phase space using kernel density estimation

Haba

2024

J. Phys.: Conf. Ser.

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Phase space is a mathematical construct that encompasses particle positions and their corresponding momenta. In general, discrete phase space structures are experimentally measured due to the limited spatial and angular resolutions of individual devices. From the perspective of beam focusing characteristics, beams are discussed in terms of core components and halo components. While the beam core is typically the primary component with low divergence, it may occasionally consist of multiple components with different velocity distributions. Mathematical modeling of the beam core in phase space is essential for accurately quantifying beam divergence and emittance. This paper presents a model that can be applied to beam cores with inner structures and reconstructs the phase space structure using kernel density interpolation. The reconstructed phase space structure is then utilized to determine beam divergence and emittance with greater precision. Additionally, these insights contribute to an enhanced understanding of beam physics.

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