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\title{Bayesian Parameter Identification for Nonlinear Systems}
\tocauthor{B. Rosic} \author{} \institute{}
{\large \underline{Bojana Rosic}}\\
TU Braunschweig\\
\\ \vspace{4mm}{\large Oliver Pajonk}\\
SPT Group GmbH Hamburg\\
\\ \vspace{4mm}{\large Anna Kucerova}\\
TU Prague\\
\\ \vspace{4mm}{\large Jan Sykora}\\
TU Prague\\
\\ \vspace{4mm}{\large Hermann G. Matthies}\\
TU Braunschweig\\
Inverse problems are important in engineering science and appear very frequently
such as for example in estimation of material porosity and
properties describing irreversible behaviour, control of high-speed machining processes etc. At present,
most of identification procedures have to cope
with ill-possedness as the problems are often considered in a deterministic framework.
However, if the parameters are modelled as random variables the process of obtaining more information
through experiments in a Bayesian setting
becomes well-posed \cite{Tarantola}. In this manner the Bayesian information update can be seen as a minimisation of
variance. In this work
we use the functional approximation of uncertainty and develop a purely deterministic procedure for the
updating process \cite{Rosic,Pajonk}. This is then contrasted to a fully Bayesian update based on Markov chain Monte Carlo \cite{Gamerman}
sampling on a few numerical nonlinear examples
based on plasticity and nonlinear diffusion models.
{\sc A. Tarantola}. { Inverse Problem Theory and Methods for Model Parameter Estimation}. Society for Industrial and Applied Mathematics, Philadelphia, 2005.
{\sc O. Pajonk and B. Rosic and A. Litvinenko and H. G. Matthies}. {A Deterministic Filter for Non-Gaussian Bayesian Estimation}. Informatikbericht 2011-04, TU Braunschweig, 2011..
{\sc B. Rosic and A. Litvinenko and O.Pajonk undefined and H. G. Matthies}. {Direct Bayesian Update of Polynomial Chaos Representations}. Informatikbericht 2011-02, TU Braunschweig, 2011..
{\sc D. Gamerman and H. F. Lopes}. {Markov Chain Monte Carlo: stochastic simulation for Bayesian inference}. Chapman and Hall, Florida.