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Automatic Differentiation and Uncertainty Analysis

The paper aims to give an overview of the possibilities for using automatic differentiation for uncertainty analysis. It presents an introduction to the general theory of automatic differentiation. Following this an overview of sensitivity analysis and nonlinear regression is given to provide the reader with a clear understanding of both general concepts and their relation to automatic differentiation. Special attention is paid to the effect of nonlinearity on the quality of the obtained estimates and it is investigated how automatic differentiation can be used to improve the estimates. Further the new concept of standard error sensitivity is introduced and formulas for efficient computation are derived. Finally the Oak system is discussed. This system is an implementation of the theory discussed in this paper using the ADOL-C library for automatic differentiation. To demonstrate the possibilities of this system several models used at the IIASA Sustainable Boreal Forests Project have been investigated.