

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 nonlinear, and even when the level of probability required makes the use of Monte Carlo techniques computationally problematic. 
CrossReferences 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 nonlinear, and even when the level of probability required makes the use of
Monte Carlo techniques computationally problematic.",
crossref = "Bucker2005ADA",
ad_area = "Uncertainty Analysis",
pages = "4758",
doi = "10.1007/3540284389_4"
}
 
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