Abstract
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 language | English |
---|---|
Title of host publication | Computational Methods for Solids and Fluids |
Subtitle of host publication | Multiscale Analysis, Probability Aspects and Model Reduction |
Editors | Adnan Ibrahimbegovic |
Place of Publication | Cham |
Publisher | Springer |
Pages | 245-286 |
Number of pages | 42 |
ISBN (Electronic) | 978-3-319-27996-1 |
ISBN (Print) | 978-3-319-27994-7 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Externally published | Yes |
Event | 2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 - Sarajevo, Bosnia and Herzegovina Duration: 10 Jun 2015 → 12 Jun 2015 Conference number: 2 |
Publication series
Name | Computational Methods in Applied Sciences |
---|---|
Publisher | Springer |
Volume | 41 |
ISSN (Print) | 1871-3033 |
Conference
Conference | 2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 |
---|---|
Country | Bosnia and Herzegovina |
City | Sarajevo |
Period | 10/06/15 → 12/06/15 |