Abstract
This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis- Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.
Original language | English |
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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 | 427-461 |
Number of pages | 35 |
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 |
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Publisher | Springer |
Volume | 41 |
ISSN (Print) | 1871-3033 |
Conference
Conference | 2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 |
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Country/Territory | Bosnia and Herzegovina |
City | Sarajevo |
Period | 10/06/15 → 12/06/15 |
Keywords
- Ensemble Kalman filter
- Markov chain Monte Carlo
- Polynomial chaos based linear Bayesian update
- Square root algorithm