Statistical detection of patterns in unidimensional distributions by continuous wavelet transforms

TL;DR

This paper introduces a wavelet transform-based method for detecting patterns such as groupings, gaps, and transitions in one-dimensional statistical distributions, with applications in astronomy and a focus on significance assessment.

Contribution

It adapts wavelet transforms for pattern detection in distributions, emphasizing noise minimization and significance evaluation, forming a flexible algorithmic pipeline.

Findings

Effective detection of distribution patterns demonstrated

Incorporates optimal noise-reduction wavelets

Provides a pipeline for analyzing single-dimensional data

Abstract

Objective detection of specific patterns in statistical distributions, like groupings or gaps or abrupt transitions between different subsets, is a task with a rich range of applications in astronomy: Milky Way stellar population analysis, investigations of the exoplanets diversity, Solar System minor bodies statistics, extragalactic studies, etc. We adapt the powerful technique of the wavelet transforms to this generalized task, making a strong emphasis on the assessment of the patterns detection significance. Among other things, our method also involves optimal minimum-noise wavelets and minimum-noise reconstruction of the distribution density function. Based on this development, we construct a self-closed algorithmic pipeline aimed to process statistical samples. It is currently applicable to single-dimensional distributions only, but it is flexible enough to undergo further generalizations and development.