Improved detection statistics for non-Gaussian gravitational wave stochastic backgrounds

Open Access

Improved detection statistics for non-Gaussian gravitational wave stochastic backgrounds

Matteo Ballelli, Riccardo Buscicchio, Barbara Patricelli, Anirban Ain, and Giancarlo Cella

Phys. Rev. D 107, 124044 – Published 23 June 2023

Abstract

In a recent paper we described a novel approach to the detection and parameter estimation of a non-Gaussian stochastic background of gravitational waves. In this work we propose an improved version of the detection procedure, preserving robustness against imperfect noise knowledge at no cost of detection performance; in the previous approach, the solution proposed to ensure robustness reduced the performances of the detection statistics, which in some cases (namely, mild non-Gaussianity) could be outperformed by Gaussian ones established in literature. We show, through a simple toy model, that the new detection statistic performs better than the previous one (and than the Gaussian statistic) everywhere in the parameter space. It approaches the optimal Neyman-Pearson statistics monotonically with increasing non-Gaussianity and/or number of detectors. In this study we discuss in detail its efficiency. This is a second, important step towards the implementation of a nearly optimal detection procedure for a realistic non-Gaussian stochastic background. We discuss the relevance of results obtained in the context of the toy model used, and their importance for understanding a more realistic scenario.

Received 21 December 2022
Revised 23 April 2023
Accepted 17 May 2023

DOI:https://doi.org/10.1103/PhysRevD.107.124044

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitational wave detection Gravitational waves

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Matteo Ballelli ^1,2, Riccardo Buscicchio ^3,4,5,*, Barbara Patricelli ^1,2, Anirban Ain ^1,2, and Giancarlo Cella ¹

¹INFN Sezione di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
²Università di Pisa, Dipartimento di Fisica “E. Fermi”, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
³Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁴INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁵Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

^*riccardo.buscicchio@unimib.it

Article Text

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Issue

Vol. 107, Iss. 12 — 15 June 2023

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Images

Figure 1
Comparison between detections statistics; each panel contains the probability of detection $P_{D}$ as a function of the number of data points $N$ . We show the “Exact,” “Improved,” “Scrambled,” and “Gaussian” statistic as solid-red, dashed-green, dashed-blue, and solid-black lines, respectively. Several different signal models are considered, parametrized by $σ_{+} / σ_{h}$ and $σ_{-} / σ_{h}$ , of increasing non-Gaussianity, going from bottom-right to top-left panel. We fix $N_{D} = 2$ and $P_{F A} = 10^{- 15}$ . Shaded red areas delimit regions with beyond-optimal performances, right-bounded by the “Exact” DS. Shaded gray area delimit statistics with performances worse than the “Gaussian” one. We observe uniform improvement over the whole parameter space of the “Improved” statistics as compared to the Gaussian one. By contrast, the scrambling procedure introduced in [12] outperforms the Gaussian one for strong non-Gaussianities, only. In Figs. 2, 4, and 5 similar results for increasing number of detectors are shown, with the “Improved” statistics approaching the “Exact” one.
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Figure 2
Comparison between detections statistics: each panel contains the probability of detection $P_{D}$ as a function of the number of datapoints $N$ . We show the “Exact,” “Improved,” “Scrambled,” and “Gaussian” statistic as solid red, dashed green, dashed blue, and solid black lines, respectively. Several diffent signal models are considered, parameterized by $σ_{+} / σ_{h}$ and $σ_{-} / σ_{h}$ , of increasing non-Gaussianity, going from bottom right to top left panel. We fix $N_{D} = 3$ and $P_{F A} = 10^{- 15}$ . Shaded red areas delimit regions with beyond-optimal performances, right-bounded by the “Exact” detections statistic. Shaded gray areas delimit statistics with performances worse than the “Gaussian” one. We observe uniform improvement over the whole parameter space of the “Improved” statistics as compared to the “Gaussian” one. By contrast, the scrambling procedure introduced in [12] outperforms the Gaussian one for strong non-Gaussianities, only.
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Figure 3
(Right panel) Contour levels of the improvement factor $N_{G} / N_{I}$ in a range of the model parameters $σ_{+} / σ_{h}$ , $σ_{-} / σ_{h}$ . Solid, dot-dashed, dashed, and dotted lines denote the improvement factor for $N_{D} = 2$ , 3, 4, 5, respectively. Pixels shading denotes the model-reduced kurtosis. We observe $N_{G} / N_{I}$ greater than one, up to a few tens, over the explored parameter space, systematically increasing for increasing number of detectors. (Left panel) The above performances are shown as a function of the reduced kurtosis and $N_{G} / N_{I}$ . Uniform grids over the signal parameter space are plotted as teal, orange, purple, and blue meshes for $N_{D} = 2$ , 3, 4 and 5, respectively. We fix as fiducial values $P_{D} = 0.5$ and $P_{F A} = 10^{- 15}$ .
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Figure 4
Comparison between the detection probability of the considered DSs as a function of the number of used data $N$ . Several different signal models are considered, parametrized by $σ_{+} / σ_{h}$ and $σ_{-} / σ_{h}$ . Here $N_{D} = 4$ and $P_{F A} = 10^{- 15}$ .
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Figure 5
Comparison between the detection probability of the considered DSs as a function of the number of used data $N$ . Several different signal models are considered, parametrized by $σ_{+} / σ_{h}$ and $σ_{-} / σ_{h}$ . Here $N_{D} = 5$ and $P_{F A} = 10^{- 15}$ .
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