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Spatial Modelling and Inference with SPDE-based GMRFs
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2011 (English)MasteroppgaveStudent thesis
Abstract [en]

In recent years, stochastic partial differential equations (SPDEs) have been shown to provide a useful way of specifying some classes of Gaussian random fields. The use of an SPDE allows for the construction of a Gaussian Markov random field (GMRF) approximation, which has very good computational properties, of the solution. In this thesis this kind of construction is considered for a specific spatial 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 matrix in the SPDE provides a way of controlling the covariance structure of the resulting GMRF. By using different diffusion matrices, it is possible to construct simple homogeneous isotropic and anisotropic fields and more interesting inhomogeneous fields. Moreover, it is possible to introduce random parameters in the coefficients of the SPDE and consider the parameters to be part of a hierarchical model. In this way one can devise a Bayesian inference scheme for the estimation of the parameters. In this thesis two different parametrizations of the diffusion matrix and corresponding parameter estimations are considered. The results show that the use of an SPDE with non-constant coefficients provides a useful way of creating inhomogeneous spatial GMRFs.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2011. , 79 p.
Keyword [no]
ntnudaim:6013, MTFYMA fysikk og matematikk, Industriell matematikk
URN: urn:nbn:no:ntnu:diva-13725Local ID: ntnudaim:6013OAI: diva2:442040
Available from: 2011-09-20 Created: 2011-09-20

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