Dimension-independent likelihood-informed MCMC

Handle URI:
http://hdl.handle.net/10754/581312
Title:
Dimension-independent likelihood-informed MCMC
Authors:
Cui, Tiangang; Law, Kody; Marzouk, Youssef M.
Abstract:
Many 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Dimension-independent likelihood-informed MCMC 2015 Journal of Computational Physics
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
8-Oct-2015
DOI:
10.1016/j.jcp.2015.10.008
Type:
Article
ISSN:
00219991
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0021999115006701
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorCui, Tiangangen
dc.contributor.authorLaw, Kodyen
dc.contributor.authorMarzouk, Youssef M.en
dc.date.accessioned2015-10-28T11:07:16Zen
dc.date.available2015-10-28T11:07:16Zen
dc.date.issued2015-10-08en
dc.identifier.citationDimension-independent likelihood-informed MCMC 2015 Journal of Computational Physicsen
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2015.10.008en
dc.identifier.urihttp://hdl.handle.net/10754/581312en
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.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0021999115006701en
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.2015.10.008en
dc.subjectMarkov chain Monte Carloen
dc.subjectLikelihood-informed subspaceen
dc.subjectInfinite-dimensional inverse problemsen
dc.subjectLangevin SDEen
dc.subjectConditioned diffusionen
dc.titleDimension-independent likelihood-informed MCMCen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Computational Physicsen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorLaw, Kodyen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.