Title: Local Two-Sample Testing: A New Tool for Analysing 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.