Show simple item record

dc.contributor.authorCui, Tiangang
dc.contributor.authorLaw, Kody
dc.contributor.authorMarzouk, Youssef M.
dc.date.accessioned2015-10-28T11:07:16Z
dc.date.available2015-10-28T11:07:16Z
dc.date.issued2015-10-08
dc.identifier.citationDimension-independent likelihood-informed MCMC 2015 Journal of Computational Physics
dc.identifier.issn00219991
dc.identifier.doi10.1016/j.jcp.2015.10.008
dc.identifier.urihttp://hdl.handle.net/10754/581312
dc.description.abstractMany Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0021999115006701
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, 8 October 2015 DOI: 10.1016/j.jcp.2015.10.008
dc.subjectMarkov chain Monte Carlo
dc.subjectLikelihood-informed subspace
dc.subjectInfinite-dimensional inverse problems
dc.subjectLangevin SDE
dc.subjectConditioned diffusion
dc.titleDimension-independent likelihood-informed MCMC
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalJournal of Computational Physics
dc.eprint.versionPost-print
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personLaw, Kody
refterms.dateFOA2017-10-08T00:00:00Z


Files in this item

Thumbnail
Name:
1-s2.0-S0021999115006701-main.pdf
Size:
1.441Mb
Format:
PDF
Description:
Accepted Manuscript

This item appears in the following Collection(s)

Show simple item record