  Describing statistical dependencies is foundational to empirical scientific
research. For uncovering intricate and possibly non-linear dependencies between
a single target variable and several source variables within a system, a
principled and versatile framework can be found in the theory of Partial
Information Decomposition (PID). Nevertheless, the majority of existing PID
measures are restricted to categorical variables, while many systems of
interest in science are continuous. In this paper, we present a novel analytic
formulation for continuous redundancy--a generalization of mutual
information--drawing inspiration from the concept of shared exclusions in
probability space as in the discrete PID definition of $I^\mathrm{sx}_\cap$.
Furthermore, we introduce a nearest-neighbor based estimator for continuous
PID, and showcase its effectiveness by applying it to a simulated energy
management system provided by the Honda Research Institute Europe GmbH. This
work bridges the gap between the measure-theoretically postulated existence
proofs for a continuous $I^\mathrm{sx}_\cap$ and its practical application to
real-world scientific problems.
