KLLR: A Scaledependent, Multivariate Model Class for Regression Analysis
Abstract
The underlying physics of astronomical systems govern the relation between their measurable properties. Consequently, quantifying the statistical relationships between systemlevel 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 modelnormalization, slope, and covariance matrixto 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 2022
 DOI:
 10.3847/15384357/ac6ac7
 arXiv:
 arXiv:2202.09903
 Bibcode:
 2022ApJ...931..166F
 Keywords:

 Astrostatistics;
 Astrostatistics tools;
 Astronomy software;
 Computational astronomy;
 Astronomy data analysis;
 1882;
 1887;
 1855;
 293;
 1858;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Statistics  Applications
 EPrint:
 The code is publicly available at https://github.com/afarahi/kllr and can be installed through `pip install kllr`