Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic

Details Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic

2006-07-05

arxiv.org/abs/gr-qc/0607015v3

Phys.Rev.D75:022003,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 8 figures, presentation and some figures modified, final version to be published in PRD

Scientific paper

10.1103/PhysRevD.75.022003

We discuss a robust data analysis method to detect a stochastic background of gravitational waves in the presence of non-Gaussian noise. In contrast to the standard cross-correlation (SCC) statistic frequently used in the stochastic background searches, we consider a {\it generalized cross-correlation} (GCC) statistic, which is nearly optimal even in the presence of non-Gaussian noise. The detection efficiency of the GCC statistic is investigated analytically, particularly focusing on the statistical relation between the false-alarm and the false-dismissal probabilities, and the minimum detectable amplitude of gravitational-wave signals. We derive simple analytic formulae for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulae, and one finds that the detection efficiency of the GCC statistic roughly corresponds to the one of the SCC statistic neglecting the contribution of non-Gaussian tails. This remarkable property is checked by performing the Monte Carlo simulations and successful agreement between analytic and simulation results was found.

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