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