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

## Abstract

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 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 formulas for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulas, 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.

- Authors:

- Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)
- Research Center for the Early Universe (RESCEU), School of Science, University of Tokyo, Tokyo 113-0033 (Japan)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20935197

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.022003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; COMPUTERIZED SIMULATION; DATA ANALYSIS; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; MONTE CARLO METHOD; PERFORMANCE; PROBABILITY; STOCHASTIC PROCESSES

### Citation Formats

```
Himemoto, Yoshiaki, Hiramatsu, Takashi, Taruya, Atsushi, Kudoh, Hideaki, and Department of Physics, University of California, Santa Barbara, California 93106.
```*Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.022003.

```
Himemoto, Yoshiaki, Hiramatsu, Takashi, Taruya, Atsushi, Kudoh, Hideaki, & Department of Physics, University of California, Santa Barbara, California 93106.
```*Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic*. United States. doi:10.1103/PHYSREVD.75.022003.

```
Himemoto, Yoshiaki, Hiramatsu, Takashi, Taruya, Atsushi, Kudoh, Hideaki, and Department of Physics, University of California, Santa Barbara, California 93106. Mon .
"Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic". United States.
doi:10.1103/PHYSREVD.75.022003.
```

```
@article{osti_20935197,
```

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

author = {Himemoto, Yoshiaki and Hiramatsu, Takashi and Taruya, Atsushi and Kudoh, Hideaki and Department of Physics, University of California, Santa Barbara, California 93106},

abstractNote = {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 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 formulas for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulas, 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.},

doi = {10.1103/PHYSREVD.75.022003},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}