Title: UKAT: Uncertainty-aware Kernel Association Test
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Hilbert-Schmidt Independence Criterion (HSIC), uncertainty-aware kernel association test

Abstract: Modern data collection methods routinely provide uncertainty estimates alongside point measurements, yet standard statistical tests typically ignore this valuable information. We introduce \texttt{UKAT} (Uncertainty-aware Kernel Association Test), a general framework for testing associations between variables while explicitly incorporating measurement uncertainties. \texttt{UKAT} treats each observation as a distribution characterized by its mean and uncertainty, then applies the Hilbert-Schmidt Independence Criterion (HSIC) to compare these distributional representations in kernel Hilbert spaces. Through extensive simulations, we demonstrate that \texttt{UKAT} achieves substantially higher statistical power than traditional association tests while maintaining proper Type I error control. We also validate \texttt{UKAT}'s versatility across diverse scientific domains in proof-of-principle applications, including detecting prompt-induced effects in large language model responses on self-reported confidence and identifying associations in physical measurements with error estimates.

TL;DR: Uncertainty-aware Kernel Association Test