Measures of Variance on Windowed Gaussian Processes

TL;DR

This paper analyzes the statistical properties of variance measures, like fractional variance and modulation index, when applied to Gaussian processes over fixed time windows, aiding in the characterization of astronomical source variability.

Contribution

It provides a comprehensive summary of the properties of variance-based variability measures for Gaussian processes, clarifying their interpretation in astronomy.

Findings

Properties of variance measures for Gaussian processes are characterized.

Insights into the interpretation of fractional variance and modulation index.

Guidance for applying variance measures in astronomical variability studies.

Abstract

The variance and fractional variance on a fixed time window (variously known as "rms percent" or "modulation index") are commonly used to characterize the variability of astronomical sources. We summarize properties of this statistic for a Gaussian process.