Quantities of interest cannot always be directly measured, but they can be linked to measurable quantities via models. In practice, both models and data suffer from inaccuracies and uncertainties. Minor inaccuracies in the models can sometimes be handled by traditional deterministic methods. However, such methods cause meaningless predictions and ill-advised decisions if model uncertainties are significant. Together with the increase in computing power, this observation has lead to the emergence of uncertainty quantification (UQ); problems previously considered deterministically are recast into a computational Bayesian framework. Compared to traditional statistics, the new aspect of UQ is to systematically account for inaccuracies in the models, i.e., in the underlying mathematical equations. As an example, mismodelling the shape of the examined body in diffuse imaging leads to severe errors in the reconstructions if the inaccurate modelling is not taken appropriately into account in the overall (statistical) model.
Currently, we focus on modelling of unknown boundary conditions in initial-boundary value problems of partial differential equations, approximate parametrizations, dealing with auxiliary uninteresting (distributed) parameters, uncertainties in the measurement settings and measurement design that tolerates these uncertainties. A particular focus lies in wave propagation related problems. Often, we employ the Bayesian approximation error approach described in the relate section under other topics in Research Areas.
Various related applications are listed under other topics in Research Areas.
Past and present collaborators
- Professor Erkki Somersalo, Case Western Reserve University, Department of Mathematics.
- Professor Daniela Calvetti, Case Western Reserve University, Department of Mathematics.
- Professor Heikki Haario, Lappeenranta University of Technology, Department of Mathematics.
- Professor Johnathan M. Bardsley, University of Montana, Department of Mathematical Sciences
- Dr. Paul Hadwin, University of Waterloo, Canada
- Dr. Ruanui Nicholson, University of California, Merced