A multiscale autocorrelation function for anisotropy studies

TL;DR

This paper introduces a new multiscale autocorrelation method for detecting anisotropy in datasets, effective even with small sample sizes and in the presence of isotropic background noise.

Contribution

The paper presents a novel scale-dependent autocorrelation procedure specifically designed for anisotropy detection, with demonstrated robustness across various dataset sizes.

Findings

Effective discrimination of anisotropy in small and large datasets

Robust performance against isotropic background contamination

Validated through simulations under different hypotheses

Abstract

In recent years many procedures have been proposed to check the anisotropy of a dataset. We present a new simple procedure, based on a scale dependent approach, to detect anisotropy signatures in a given distribution with particular attention to small dataset. The method provides a good discrimination power for both large and small datasets, even in presence of strong contaminating isotropic background. We present some applications to simulated datasets of events to investigate statistical features of the method and present and inspect its behavior under both the null or the alternative hypothesis.