2006 | OriginalPaper | Buchkapitel
Automatic Propagation of Uncertainties
verfasst von : Bruce Christianson, Maurice Cox
Erschienen in: Automatic Differentiation: Applications, Theory, and Implementations
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.