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Automatic Propagation of Uncertainties

- incollection -
 

Area
Uncertainty Analysis

Author(s)
Bruce Christianson , Maurice Cox

Published in
Automatic Differentiation: Applications, Theory, and Implementations

Editor(s)
H. M. Bücker, G. Corliss, P. Hovland, U. Naumann, B. Norris

Year
2005

Publisher
Springer

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.

Cross-References
Bucker2005ADA

BibTeX
@INCOLLECTION{
         Christianson2005APo,
       author = "Bruce Christianson and Maurice Cox",
       title = "Automatic Propagation of Uncertainties",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       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.",
       crossref = "Bucker2005ADA",
       ad_area = "Uncertainty Analysis",
       pages = "47--58",
       doi = "10.1007/3-540-28438-9_4"
}


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