Local Two-Sample Testing: A New Tool for Analysing High-Dimensional Astronomical Data

TL;DR

This paper introduces a local two-sample hypothesis testing framework for analyzing high-dimensional astronomical data directly in its native space, enabling detailed local comparisons of galaxy properties without dimensionality reduction.

Contribution

It presents a novel local two-sample testing method applicable to high-dimensional data, demonstrated on galaxy morphological and physical properties from HST observations.

Findings

Identified regions where high-mass galaxies are more prevalent than low-mass ones.

Detected areas with higher star-formation rates associated with more extended or disturbed galaxies.

Showed the method's effectiveness in revealing local differences in high-dimensional astronomical data.

Abstract

Modern surveys have provided the astronomical community with a flood of high-dimensional data, but analyses of these data often occur after their projection to lower-dimensional spaces. In this work, we introduce a local two-sample hypothesis test framework that an analyst may directly apply to data in their native space. In this framework, the analyst defines two classes based on a response variable of interest (e.g. higher-mass galaxies versus lower-mass galaxies) and determines at arbitrary points in predictor space whether the local proportions of objects that belong to the two classes significantly differs from the global proportion. Our framework has a potential myriad of uses throughout astronomy; here, we demonstrate its efficacy by applying it to a sample of 2487 i-band-selected galaxies observed by the HST ACS in four of the CANDELS program fields. For each galaxy, we have seven morphological summary statistics along with an estimated stellar mass and star-formation rate. We perform two studies: one in which we determine regions of the seven-dimensional space of morphological statistics where high-mass galaxies are significantly more numerous than low-mass galaxies, and vice-versa, and another study where we use SFR in place of mass. We find that we are able to identify such regions, and show how high-mass/low-SFR regions are associated with concentrated and undisturbed galaxies while galaxies in low-mass/high-SFR regions appear more extended and/or disturbed than their high-mass/low-SFR counterparts.