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dc.contributor.author
Hoang, Viet Ha
dc.contributor.author
Schwab, Christoph
dc.contributor.author
Stuart, Andrew M.
dc.date.accessioned
2022-09-19T08:25:58Z
dc.date.available
2022-09-19T08:25:58Z
dc.date.issued
2012-08
dc.identifier.uri
http://hdl.handle.net/20.500.11850/571308
dc.identifier.doi
10.3929/ethz-a-010395062
dc.description.abstract
Several classes of MCMC methods for the numerical solution of Bayesian Inverse Problems for partial differential equations (PDEs) with unknown random field coefficients are considered. A general framework for their numerical analysis is presented. The complexity of MCMC sampling for the unknown fields from the posterior density, as well as the convergence of the discretization error of the PDE of interest in the forward response map, is analyzed. Particular attention is given to bounds on the overall work required by the MCMC algorithms for achieving a prescribed error level E. We show that the computational complexity of straightforward combinations of MCMC sampling strategies with standard PDE solution methods is generally excessive. Two computational strategies for substantially reducing the computational complexity of MCMC methods for Bayesian inverse problems prising in PDEs are studied: a parametric, deterministic gpc-type (generalized polynomial chaos) representation of the forward solution map of the PDE with uncertain coefficients, which has been proposed and implemented in the engineering literature (e.g. [17, 15, 16]); and a new Multi-Level Monte Carlo sampling strategy of the Markov Chain (MLMCMC) with sampling from a multilevel discretization of the posterior and a multilevel discretization of the forward PDE. We compare the computational complexity of these gpc-MCMC and MLMCMC methods to that of the plain MCMC method, and provide sufficient conditions on the regularity of the unknown coefficient for both, the gpc-MCMC and MLMCMC method, to afford substantial complexity reductions over the plain MCMC approach.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.title
Sparse MCMC gpc Finite Element Methods for Bayesian Inverse Problems
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
SAM Research Report
ethz.journal.volume
2012-23
en_US
ethz.size
36 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.grant
Automated Urban Parking and Driving
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=466
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-10T11:38:20Z
ethz.source
ECOL
ethz.source
ECIT
ethz.identifier.importid
imp59366b707d97869597
ethz.identifier.importid
imp5936500cc2b4166689
ethz.ecolpid
eth:47426
ethz.ecitpid
pub:94793
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2022-09-19T08:26:07Z
ethz.rosetta.lastUpdated
2022-09-19T08:26:07Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/154954
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/59267
ethz.COinS
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