Haar wavelets as a tool for the statistical characterization of variability

TL;DR

This paper introduces a Haar wavelet-based method for statistically characterizing variability in noisy gamma-ray light-curve data, effectively distinguishing genuine signals from background noise.

Contribution

The paper presents a novel application of Haar wavelet decomposition to assess variability significance in gamma-ray astronomy data, addressing challenges of noise and trial factors.

Findings

Effective in identifying variability in simulated data

Successfully applied to real M87 light curve data

Provides confidence levels for variability detection

Abstract

In the field of gamma-ray astronomy, irregular and noisy datasets make difficult the characterization of light-curve features in terms of statistical significance while properly accounting for trial factors associated with the search for variability at different times and over different timescales. In order to address these difficulties, we propose a method based on the Haar wavelet decomposition of the data. It allows statistical characterization of possible variability, embedded in a white noise background, in terms of a confidence level. The method is applied to artificially generated data for characterization as well as to the the very high energy M87 light curve recorded with VERITAS in 2008 which serves here as a realistic application example.