On the (In)Efficiency of the Cross-Correlation Statistic for Gravitational Wave Stochastic Background Signals with Non-Gaussian Noise and Heterogeneous Detector Sensitivities

TL;DR

This paper evaluates the effectiveness of the standard cross-correlation statistic for gravitational wave background detection, especially when detector sensitivities vary and noise distributions are non-Gaussian, proposing an alternative statistic for improved sensitivity.

Contribution

It introduces and analyzes an alternative detection statistic that outperforms the standard in scenarios with heterogeneous detector sensitivities and non-Gaussian noise.

Findings

Detector sensitivity differences greatly affect statistic efficiency.

The alternative statistic outperforms the standard when sensitivities differ by an order of magnitude.

Non-Gaussian signals have minimal impact on the relative efficiency of the statistics.

Abstract

Under standard assumptions including stationary and serially uncorrelated Gaussian gravitational wave stochastic background signal and noise distributions, as well as homogenous detector sensitivities, the standard cross-correlation detection statistic is known to be optimal in the sense of minimizing the probability of a false dismissal at a fixed value of the probability of a false alarm. The focus of this paper is to analyze the comparative efficiency of this statistic, versus a simple alternative statistic obtained by cross-correlating the \textit{squared} measurements, in situations that deviate from such standard assumptions. We find that differences in detector sensitivities have a large impact on the comparative efficiency of the cross-correlation detection statistic, which is dominated by the alternative statistic when these differences reach one order of magnitude. This effect holds even when both the signal and noise distributions are Gaussian. While the presence of non-Gaussian signals has no material impact for reasonable parameter values, the relative inefficiency of the cross-correlation statistic is less prominent for fat-tailed noise distributions but it is magnified in case noise distributions have skewness parameters of opposite signs. Our results suggest that introducing an alternative detection statistic can lead to noticeable sensitivity gains when noise distributions are possibly non-Gaussian and/or when detector sensitivities exhibit substantial differences, a situation that is expected to hold in joint detections from Advanced LIGO and Advanced Virgo, in particular in the early phases of development of the detectors, or in joint detections from Advanced LIGO and Einstein Telescope.