Spatial Modelling and Inference with SPDE-based GMRFs
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
Place, publisher, year, edition, pages
Institutt for matematiske fag , 2011. , 79 p.
ntnudaim:6013, MTFYMA fysikk og matematikk, Industriell matematikk
IdentifiersURN: urn:nbn:no:ntnu:diva-13725Local ID: ntnudaim:6013OAI: oai:DiVA.org:ntnu-13725DiVA: diva2:442040
Rue, Håvard, ProfessorLindgren, Finn