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By  and J. O. RamsayG. Hooker, D. Campbell, J. Cao and J. O. Ramsay


University for instruction in the language and principles of chemical engineering, many consultations and much useful advice. Appreciation is also due to the referees, whose comments on an earlier version of the paper have been invaluable. Summary. We propose a new method for estimating parameters in models de ned by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behavior of derivatives of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. This paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters de ning a system of nonlinear differential equations. The approach is based on a modi cation of data smoothing methods along with a generalization of pro led estimation. We derive estimates and con dence intervals, and show that these have low bias and good coverage properties, respectively, for data simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated using real-world data from chemistry and from the progress of the auto-immune disease lupus

Topics: 1. Challenges in dynamic systems estimation
Year: 2011
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