Inverse problems in a Bayesian setting

Hermann G. Matthies*, Elmar Zander, Bojana V. Rosić, Alexander Litvinenko, Oliver Pajonk

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

25 Citations (Scopus)
31 Downloads (Pure)


In a Bayesian setting, inverse problems and uncertainty quantification (UQ)-the propagation of uncertainty through a computational (forward) model- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

Original languageEnglish
Title of host publicationComputational Methods for Solids and Fluids
Subtitle of host publicationMultiscale Analysis, Probability Aspects and Model Reduction
EditorsAdnan Ibrahimbegovic
Place of PublicationCham
Number of pages42
ISBN (Electronic)978-3-319-27996-1
ISBN (Print)978-3-319-27994-7
Publication statusPublished - 1 Jan 2016
Externally publishedYes
Event2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 - Sarajevo, Bosnia and Herzegovina
Duration: 10 Jun 201512 Jun 2015
Conference number: 2

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033


Conference2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015
Country/TerritoryBosnia and Herzegovina


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