Adaptive approximation of higher order posterior statistics

Handle URI:
http://hdl.handle.net/10754/597451
Title:
Adaptive approximation of higher order posterior statistics
Authors:
Lee, Wonjung
Abstract:
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.
Citation:
Lee W (2014) Adaptive approximation of higher order posterior statistics. Journal of Computational Physics 258: 833–855. Available: http://dx.doi.org/10.1016/j.jcp.2013.11.015.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Feb-2014
DOI:
10.1016/j.jcp.2013.11.015
Type:
Article
ISSN:
0021-9991
Sponsors:
The author thanks Dr. Chris Farmer for helpful discussions and suggestions. The author also thanks King Abdullah University of Science and Technology (KAUST) Award No. KUK-C1-013-04 for its financial support of this research.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLee, Wonjungen
dc.date.accessioned2016-02-25T12:33:30Zen
dc.date.available2016-02-25T12:33:30Zen
dc.date.issued2014-02en
dc.identifier.citationLee W (2014) Adaptive approximation of higher order posterior statistics. Journal of Computational Physics 258: 833–855. Available: http://dx.doi.org/10.1016/j.jcp.2013.11.015.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2013.11.015en
dc.identifier.urihttp://hdl.handle.net/10754/597451en
dc.description.abstractFiltering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.en
dc.description.sponsorshipThe author thanks Dr. Chris Farmer for helpful discussions and suggestions. The author also thanks King Abdullah University of Science and Technology (KAUST) Award No. KUK-C1-013-04 for its financial support of this research.en
dc.publisherElsevier BVen
dc.subjectData assimilationen
dc.subjectNonlinear filteringen
dc.subjectUncertainty quantificationen
dc.subjectWiener chaos expansionen
dc.titleAdaptive approximation of higher order posterior statisticsen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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