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A finite element method for densityestimation with Gaussian process priors

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Griebel, Michael; Hegland, Markus

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A variational problem characterizing the density estimator defined by the maximum a posteriori method with Gaussian process priors is derived. It is shown that this problem is well posed and can be solved with Newton's method. Numerically, the solution is approximated by a Galerkin/finite element method with piecewise multilinear functions on uniform grids. Error bounds for this method are given and numerical experiments are performed for one-, two-, and three-dimensional examples.

dc.contributor.authorGriebel, Michael
dc.contributor.authorHegland, Markus
dc.date.accessioned2015-12-07T22:21:19Z
dc.identifier.issn0036-1429
dc.identifier.urihttp://hdl.handle.net/1885/19991
dc.description.abstractA variational problem characterizing the density estimator defined by the maximum a posteriori method with Gaussian process priors is derived. It is shown that this problem is well posed and can be solved with Newton's method. Numerically, the solution is approximated by a Galerkin/finite element method with piecewise multilinear functions on uniform grids. Error bounds for this method are given and numerical experiments are performed for one-, two-, and three-dimensional examples.
dc.publisherSIAM Publications
dc.sourceSIAM Journal of Numerical Analysis
dc.subjectKeywords: Error analysis; Finite element method; Galerkin methods; Gaussian distribution; Gaussian noise (electronic); Newton-Raphson method; Density estimation; Density estimator; Gaussian process priors; Maximum a posteriori methods; Multilinear functions; Newton Density estimation; Finite elements; Galerkin; Newton
dc.titleA finite element method for densityestimation with Gaussian process priors
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume47
dc.date.issued2010
local.identifier.absfor010101 - Algebra and Number Theory
local.identifier.ariespublicationu5035478xPUB10
local.type.statusPublished Version
local.contributor.affiliationGriebel, Michael, University of Bonn
local.contributor.affiliationHegland, Markus, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue6
local.bibliographicCitation.startpage4759
local.bibliographicCitation.lastpage4792
local.identifier.doi10.1137/080736478
dc.date.updated2016-02-24T11:33:19Z
local.identifier.scopusID2-s2.0-79961038273
local.identifier.thomsonID000277836100032
CollectionsANU Research Publications

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