Abstract
Motivated by problems in metrology, we consider a numerical evaluation program y = f(x) as a model for a measurement process. We use a probability density function to represent the uncertainties in the inputs x and examine some of the consequences of using Automatic Differentiation to propagate these uncertainties to the outputs y.We show how to use a combination of Taylor series propagation and interval partitioning to obtain coverage (confidence) intervals and ellipsoids based on unbiased estimators for means and covariances of the outputs, even where f is sharply non-linear, and even when the level of probability required makes the use of Monte Carlo techniques computationally problematic.
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© 2006 Springer
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Christianson, B., Cox, M. (2006). Automatic Propagation of Uncertainties. In: Bücker, M., Corliss, G., Naumann, U., Hovland, P., Norris, B. (eds) Automatic Differentiation: Applications, Theory, and Implementations. Lecture Notes in Computational Science and Engineering, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28438-9_4
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DOI: https://doi.org/10.1007/3-540-28438-9_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28403-1
Online ISBN: 978-3-540-28438-3
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