%0 Journal Article %A Kostina, Ekaterina %A Nattermann, Max %D 2015 %I Begell House %K uncertainty quantification, representing of uncertainty, inverse problems, parameter estimation, maximum likelihood, stochastic sensitivity analysis %N 3 %P 209-231 %R 10.1615/Int.J.UncertaintyQuantification.2015010312 %T SECOND-ORDER SENSITIVITY ANALYSIS OF PARAMETER ESTIMATION PROBLEMS %U https://www.dl.begellhouse.com/journals/52034eb04b657aea,7348f81710c4fb51,5859e5395b9ef185.html %V 5 %X 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. %8 2015-08-14