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.
CITATION STYLE
Christianson, B., & Cox, M. (2006). Automatic Propagation of Uncertainties. Lecture Notes in Computational Science and Engineering, 50, 47–58. https://doi.org/10.1007/3-540-28438-9_4
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