KLLR: A scale-dependent, multivariate model class for regression
  analysis
  The underlying physics of astronomical systems governs the relation between
their measurable properties. Consequently, quantifying the statistical
relationships between system-level observable properties of a population offers
insights into the astrophysical drivers of that class of systems. While purely
linear models capture behavior over a limited range of system scale, the fact
that astrophysics is ultimately scale-dependent implies the need for a more
flexible approach to describing population statistics over a wide dynamic
range. For such applications, we introduce and implement a class of
Kernel-Localized Linear Regression (KLLR) models. KLLR is a natural extension
to the commonly-used linear models that allows the parameters of the linear
model -- normalization, slope, and covariance matrix -- to be scale-dependent.
KLLR performs inference in two steps: (1) it estimates the mean relation
between a set of independent variables and a dependent variable and; (2) it
estimates the conditional covariance of the dependent variables given a set of
independent variables. We demonstrate the model's performance in a simulated
setting and showcase an application of the proposed model in analyzing the
baryonic content of dark matter halos. As a part of this work, we publicly
release a Python implementation of the KLLR method.
