Abstract
Computational uncertainty quantification in a probabilistic setting is a special case of a parametric problem. Parameter dependent state vectors lead via association to a linear operator to analogues of covariance, its spectral decomposition, and the associated Karhunen-Loève expansion. From this one obtains a generalised tensor representation The parameter in question may be a tuple of numbers, a function, a stochastic process, or a random tensor field. The tensor factorisation may be cascaded, leading to tensors of higher degree. When carried on a discretised level, such factorisations in the form of low-rank approximations lead to very sparse representations of the high dimensional quantities involved. Updating of uncertainty for new information is an important part of uncertainty quantification. Formulated in terms or random variables instead of measures, the Bayesian update is a projection and allows the use of the tensor factorisations also in this case.
Original language | English |
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Title of host publication | Uncertainty Quantification in Scientific Computing |
Subtitle of host publication | 10th IFIP WG 2.5 Working Conference, WoCoUQ 2011, Revised Selected Papers |
Editors | Andrew M. Dienstfrey, Ronald F. Boisvert |
Place of Publication | Berlin, Heidelberg |
Publisher | Springer |
Pages | 139-150 |
Number of pages | 12 |
ISBN (Electronic) | 978-3-642-32677-6 |
ISBN (Print) | 978-3-642-32676-9 |
DOIs | |
Publication status | Published - 1 Jan 2012 |
Externally published | Yes |
Event | 10th IFIP WG 2.5 Working Conference on Uncertainty Quantification in Scientific Computing, WoCoUQ 2011 - Boulder, United States Duration: 1 Aug 2011 → 4 Aug 2011 Conference number: 10 |
Publication series
Name | IFIP Advances in Information and Communication Technology |
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Publisher | Springer |
Volume | 377 |
ISSN (Print) | 1868-4238 |
ISSN (Electronic) | 1861-2288 |
Conference
Conference | 10th IFIP WG 2.5 Working Conference on Uncertainty Quantification in Scientific Computing, WoCoUQ 2011 |
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Abbreviated title | WoCoUQ |
Country/Territory | United States |
City | Boulder |
Period | 1/08/11 → 4/08/11 |
Keywords
- Bayesian updating
- low-rank tensor approximation
- parametric problems
- uncertainty quantification