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dc.contributor.advisorRue, Håvardnb_NO
dc.contributor.advisorLindgren, Finnnb_NO
dc.contributor.authorFuglstad, Geir-Arnenb_NO
dc.date.accessioned2014-12-19T13:59:33Z
dc.date.available2014-12-19T13:59:33Z
dc.date.created2011-09-20nb_NO
dc.date.issued2011nb_NO
dc.identifier442040nb_NO
dc.identifierntnudaim:6013nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/258930
dc.description.abstractIn recent years, stochastic partial differential equations (SPDEs) have been shown to provide a usefulway of specifying some classes of Gaussian random fields. The use of an SPDEallows for the construction of a Gaussian Markov random field (GMRF) approximation, which has verygood computational properties, of the solution.In this thesis this kind of construction is considered for a specificspatial SPDE with non-constant coefficients, a form of diffusion equation driven by Gaussian white noise. The GMRF approximation is derived from the SPDE by a finite volume method. The diffusion matrixin the SPDE provides a way of controlling the covariancestructure of the resulting GMRF.By using different diffusion matrices, itis possible to construct simple homogeneous isotropic and anisotropic fields and more interesting inhomogeneous fields. Moreover, it is possible to introduce random parametersin the coefficients of the SPDE and consider the parametersto be part of a hierarchical model. In this way onecan devise a Bayesian inference scheme for theestimation of the parameters. In this thesis twodifferent parametrizations of the diffusion matrixand corresponding parameter estimations are considered.The results show that the use of an SPDE with non-constant coefficients provides a useful way of creating inhomogeneousspatial GMRFs.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for matematiske fagnb_NO
dc.subjectntnudaim:6013no_NO
dc.subjectMTFYMA fysikk og matematikkno_NO
dc.subjectIndustriell matematikkno_NO
dc.titleSpatial Modelling and Inference with SPDE-based GMRFsnb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber79nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fagnb_NO


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