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"
}