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Lors du séminaire du Labex MS2T du 6 mai 2015, nous avons eu le plaisir d’écouter un exposé de Hermann Matthies, Professeur au sein de Carl-Friedrich-Gauss Faculty et Directeur de l’ Institute of Scientific Computing at Technische Universität Braunschweig, Allemagne, sur le thème :

Identification, Uncertainty Quantification and Bayesian Updating

Résumé de l’exposé :

In inverse problems and identification procedures, there are unknown – and usually not directly observable quantities, which have to be inferred from observations which are only indirectly linked to these unknown quantities. If these unknown quantities and our knowledge/information about them is modelled with the methods of probability theory, then it is possible to use methods based on Bayes´s theory to condition on the knowledge description on these indirect observations.
The mathematical framework for such a computational task will be sketched, and it turns out that the crucial component is the ability to predict in mathematical models the effect of „input“ uncertaintes onto „output/observable“ quantities. This „uncertainty quantification“ can in principle be done with Monte Carlo methods, but they are often very slow. Here we use „functional approximations“, where the unknown random quantities are expressed as functions of known random variables. The mathematical framework for this will be explained.