Statistics of time and frequency-averaged spectra in gravitational-wave background searches

TL;DR

This paper investigates the validity of assuming uncorrelated time and frequency segments in gravitational-wave background searches, introducing analytical tools to quantify errors from averaging and addressing optimal data segmentation.

Contribution

It provides a Fisher information-based framework to evaluate the impact of averaging on parameter inference in gravitational-wave data analysis.

Findings

A new analytical method to estimate errors from averaging.

Insights into optimal time chunking for stationary processes.

Quantitative assessment of correlation effects in spectral analysis.

Abstract

Time series analysis from gravitational-wave detectors often relies on the assumption that time chunks, or frequency bins, are uncorrelated. We discuss the validity of this approximation in the context of searches for stochastic gravitational-wave backgrounds. We examine the impact of averaging over time and frequency, a reduction technique commonly employed to minimize the computational expense of likelihood evaluations. We introduce an analytical tool based on Fisher information to quantify the error in parameter inference arising from ignoring these effects. Finally, we address the issue of locally stationary processes and optimal time chunking.