title: Error bounds for data-driven models of dynamical systems.
abstract: This work provides a technique for estimating error bounds about the predictions of data-driven models of dynamical systems. The bootstrap technique is applied to predictions from a set of dynamical system models, rather than from the time-series data, to estimate the reliability (in the form of prediction intervals) for each prediction. The technique is illustrated using human core temperature data, modeled by a hybrid (autoregressive plus first principles) approach. The temperature prediction intervals obtained are in agreement with those from the Camp-Meidell inequality. Moreover, as expected, the prediction intervals increase with the prediction horizon, time-series data variability, and model inaccuracy.
authors.affiliation: Bioinformatics Cell, U.S. Army Medical Research and Materiel Command, Frederick, MD 21702, USA.
authors.forename: Nicholas O
authors.initials: NO
authors.lastname: Oleng'
authors.forename: Andrei
authors.initials: A
authors.lastname: Gribok
authors.forename: Jaques
authors.initials: J
authors.lastname: Reifman
mesh_terms: D000465:Algorithms; D001831:Body Temperature / Q000502:physiology; D003198:Computer Simulation; D016001:Confidence Intervals; D005080:Exercise Test; D005544:Forecasting; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D011336:Probability; D012044:Regression Analysis; D015203:Reproducibility of Results; D016008:Statistical Distributions; D013821:Thermometers; D016138:Walking / Q000502:physiology