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

TL;DR

This paper introduces a generalized cross-correlation statistic for detecting stochastic gravitational wave backgrounds amidst non-Gaussian noise, demonstrating its near-optimal performance and robustness through analytical derivations and Monte Carlo simulations.

Contribution

The paper develops and analytically evaluates a generalized cross-correlation statistic that outperforms standard methods in non-Gaussian noise environments for gravitational wave detection.

Findings

GCC statistic is nearly optimal even with non-Gaussian noise.

Analytic formulas for false-alarm and false-dismissal probabilities are derived.

Monte Carlo simulations confirm the analytic predictions.

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 {\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.