Pan, GuanruGuanruPanReinhardt, DirkDirkReinhardtGros, SebastienSebastienGrosFaulwasser, TimmTimmFaulwasser2026-06-152026-06-152026-05-15arXiv: 2605.15851 (2026)https://hdl.handle.net/11420/63498This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.eneess.SYTechnology::600: TechnologyPreprint10.48550/arXiv.2605.158512605.15851