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dc.contributor.author
Schillings, Claudia
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2022-09-19T08:55:15Z
dc.date.available
2022-09-19T08:55:15Z
dc.date.issued
2013-06
dc.identifier.uri
http://hdl.handle.net/20.500.11850/571331
dc.identifier.doi
10.3929/ethz-a-010389584
dc.description.abstract
We establish posterior sparsity in Bayesian inversion for systems with distributed parameter uncertainty subject to noisy data. We generalize the particular case of scalar diffusion problems with random coefficients in [29] to broad classes of operator equations. For countably parametric, deterministic representations of uncertainty in the forward problem which belongs to a certain sparsity class, we quantify analytic regularity of the (countably parametric) Bayesian posterior density and prove that the parametric, deterministic density of the Bayesian posterior belongs to the same sparsity class. Generalizing [32, 29], the considered forward problems are parametric, deterministic operator equations, and computational Bayesian inversion is to evaluate expectations of quantities of interest (QoIs) under the Bayesian posterior, conditional on given data. The sparsity results imply, on the one hand, sparsity of Legendre (generalized) polynomial chaos expansions of the Bayesian posterior and, on the other hand, convergence rates for data-adaptive Smolyak integration algorithms for computational Bayesian estimation which are independent of dimension of the parameter space. The convergence rates are, in particular, superior to Markov Chain Monte-Carlo sampling of the posterior, in terms of the number N of instances of the parametric forward problem to be solved.
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.subject
Bayesian Inverse Problems
en_US
dc.subject
Parametric Operator Equations
en_US
dc.subject
Smolyak Quadrature
en_US
dc.subject
Sparsity
en_US
dc.subject
Uniform Prior Measures
en_US
dc.title
Sparsity in Bayesian Inversion of Parametric Operator Equations
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
SAM Research Report
ethz.journal.volume
2013-17
en_US
ethz.size
45 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=513
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-11T03:57:52Z
ethz.source
ECOL
ethz.source
ECIT
ethz.identifier.importid
imp59366b6fc82ac57510
ethz.identifier.importid
imp59365189279d497233
ethz.ecolpid
eth:47399
ethz.ecitpid
pub:124468
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2022-09-19T08:55:27Z
ethz.rosetta.lastUpdated
2023-02-07T06:23:59Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/154935
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/79179
ethz.COinS
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