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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015010312
pages 209-231

SECOND-ORDER SENSITIVITY ANALYSIS OF PARAMETER ESTIMATION PROBLEMS

Ekaterina Kostina
Institute for Apllied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, 69120 Heidelberg, Germany
Max Nattermann
Institute for Apllied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, 69120 Heidelberg, Germany

ABSTRACT

The use of model-based simulation to gain knowledge of unknown phenomena and processes behavior is a challenging task in many natural sciences. In order to get a full description of an underlying process, an important issue is to estimate unknown parameters from real but erroneous observations. Thus the whole system is affected by uncertainties and a sensitivity analysis is necessary. Usually one applies first-order sensitivity analysis and resulting linearized confidence regions to determine the statistical accuracy of the solution to parameter estimation problems. But especially in significantly nonlinear cases linearized regions may not be an adequate representation. In this paper, we suggest quadratic regions based on the second-order sensitivity analysis. The new region definition is based on a map that transforms the input uncertainties onto the parameter space. Furthermore, the approximation accuracy of the quadratic confidence regions is exemplary illustrated at two examples.