<div class="csl-bib-body">
<div class="csl-entry">Stadlbauer, B. (2018). <i>Fast algorithms for iterative Bayesian PDE inversion</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.56613</div>
</div>
-
dc.identifier.uri
https://doi.org/10.34726/hss.2018.56613
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/6999
-
dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
-
dc.description.abstract
In this article we present algorithms to perform Bayesian inversion based on physical models, in particular based on partial differential equations. We are interested in identifying parameters of the PDEs that affect functionals of the solutions for which experimental data are available. Markov-chain Monte-Carlo methods like the Metropolis algorithm provide the algorithmic foundation. We present an adaptation and extension of this procedure to be able to perform multi-dimensional Bayesian inversion where not all measurements have to be present prior to the estimation, but become available in batches as time passes. Namely, based on the Delayed-Rejection Adaptive-Metropolis (DRAM) algorithm, we introduce an iterative approach, where we use the posterior of the last Metropolis run as the prior for the new run, where we use new measurements in each iteration. This allows to examine some information about the parameters already during the estimation process. Therefore a density estimator needs to be introduced. We make use of the Improved Fast Gauss Transform (IFGT) which allows us to perform a faster evaulation of the kernel density estimator, reducing the runtime from quadratic to nearly linear. Applications using a nano-capacitor sensor array are presented as well, where we estimate the radii of over 4000 nano-electrodes.
en
dc.language
English
-
dc.language.iso
en
-
dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
-
dc.subject
Bayesian Estimation
en
dc.subject
PDE Inversion
en
dc.subject
Iterative Metropolis
en
dc.title
Fast algorithms for iterative Bayesian PDE inversion
en
dc.title.alternative
Bayessche inverse PDE Probleme
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.56613
-
dc.contributor.affiliation
TU Wien, Österreich
-
dc.rights.holder
Benjamin Stadlbauer
-
dc.publisher.place
Wien
-
tuw.version
vor
-
tuw.thesisinformation
Technische Universität Wien
-
tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
-
dc.type.qualificationlevel
Diploma
-
dc.identifier.libraryid
AC15188969
-
dc.description.numberOfPages
27
-
dc.identifier.urn
urn:nbn:at:at-ubtuw:1-117239
-
dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
-
item.openaccessfulltext
Open Access
-
item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
-
item.grantfulltext
open
-
item.mimetype
application/pdf
-
item.languageiso639-1
en
-
item.openairetype
master thesis
-
item.fulltext
with Fulltext
-
item.cerifentitytype
Publications
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing