Bayesian methods via spectral functional representations

Abstract:

The state or parameter estimation given observations of a physical system is generally an ill-posed inverse problem. The solution often does not exist, it is not unique and it is highly sensitive on the data perturbations. To resolve this issue, the deterministic identification procedures use different kinds of regularisation techniques which as a final result deliver a point estimate of the solution. However, the deterministic algorithms fully ignore the presence of uncertainty in a solution and its possible non-uniqueness. On the other hand, the inverse problem seen in a probabilistic Bayesian point of view does not encounter these difficulties. In this work the conditional expectation view on Bayesian inference is advocated via purely functional approximation procedure for the updating process of not only linear but also nonlinear problems|linear and nonlinear spectral based Bayesian identi cation. This is then contrasted to a fully Bayesian update based on Markov chain Monte Carlo sampling on a few numerical examples.

Biography:

Dr. Bojana Rosic, born 16.08.1982 in Kragujevac, Serbia, is postdoctoral researcher and lecturer at Technische Universität Braunschweig, Lower Saxony, Germany. She obtained her master and magister (Master of Philosophy) degrees in mechatronics, University of Kragujevac Serbia, and dual doctoral degree in applied mathematics and applied engineering, Technische Universität Braunschweig (Germany) and University of Kragujevac (Serbia). Her study and research engagement led to Best Student Award of Engineering Science of the Republic of Serbia and GACM (German Association of Computational Mechanics) award for the best PhD thesis among others. She was GAMM (German Association of Applied Mathematics and Mechanics) Junior representative in time period 2013-2016. Her research interests include modelling of irrerversible material phenomena, uncertainty quanti cation, inverse problems in probabilistic se tting, modelling of heterogeneous materials, multiscale problems and optimal control.