Spatial inference for nonlattice data using Markov Random fields
(2004) Abstract
 This thesis deals with how computationally effective lattice models could be used for inference of data with a continuous spatial index. The fundamental idea is to approximate a Gaussian field with a Gaussian Markov random field (GMRF) on a lattice. Using a bilinear interpolation at nonlattice locations we get a reasonable model also at nonlattice locations. We can thus exploit the computational benefits of a lattice model even for data with continuous spatial index.
In Paper A, a GMRF model is used in a Bayesian approach for prediction of a spatial random field. A hierarchical parametric model is setup, and inference is made by Markov Chain Monte Carlo simulations. In this way we obtain predictors and estimated... (More)  This thesis deals with how computationally effective lattice models could be used for inference of data with a continuous spatial index. The fundamental idea is to approximate a Gaussian field with a Gaussian Markov random field (GMRF) on a lattice. Using a bilinear interpolation at nonlattice locations we get a reasonable model also at nonlattice locations. We can thus exploit the computational benefits of a lattice model even for data with continuous spatial index.
In Paper A, a GMRF model is used in a Bayesian approach for prediction of a spatial random field. A hierarchical parametric model is setup, and inference is made by Markov Chain Monte Carlo simulations. In this way we obtain predictors and estimated prediction uncertainties as well as estimates of model parameters. The spatial correlation is modelled as a GMRF on a lattice which is interpolated between lattice points. The methods are tested on a data set of Calcium content in forest soils of southern Sweden.
In Paper B, we develop a methodology for kriging large data sets. By approximating a full Gaussian model with an interpolated GMRF the kriging weights can be calculated with less computation. For n observations and a full model, calculation of the kriging weights requires inversion of an n x n covariance matrix. Approximating the model with a GMRF defined on an N x N lattice, the computations can be reduced to inversion of an NxN band limited matrix. For large data sets the full
n x n matrix might not be possible to invert, and the GMRF approximation is then not only time saving, but is what makes it possible to perform kriging with the full data set. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/753396
 author
 Werner Hartman, Linda ^{LU}
 supervisor

 Ola Hössjer ^{LU}
 organization
 publishing date
 2004
 type
 Thesis
 publication status
 published
 subject
 language
 English
 LU publication?
 yes
 id
 e433ca170fb349cda4d9e9933530c9b6 (old id 753396)
 date added to LUP
 20080104 14:20:26
 date last changed
 20160919 08:45:19
@misc{e433ca170fb349cda4d9e9933530c9b6, abstract = {This thesis deals with how computationally effective lattice models could be used for inference of data with a continuous spatial index. The fundamental idea is to approximate a Gaussian field with a Gaussian Markov random field (GMRF) on a lattice. Using a bilinear interpolation at nonlattice locations we get a reasonable model also at nonlattice locations. We can thus exploit the computational benefits of a lattice model even for data with continuous spatial index.<br/><br> <br/><br> In Paper A, a GMRF model is used in a Bayesian approach for prediction of a spatial random field. A hierarchical parametric model is setup, and inference is made by Markov Chain Monte Carlo simulations. In this way we obtain predictors and estimated prediction uncertainties as well as estimates of model parameters. The spatial correlation is modelled as a GMRF on a lattice which is interpolated between lattice points. The methods are tested on a data set of Calcium content in forest soils of southern Sweden.<br/><br> <br/><br> In Paper B, we develop a methodology for kriging large data sets. By approximating a full Gaussian model with an interpolated GMRF the kriging weights can be calculated with less computation. For n observations and a full model, calculation of the kriging weights requires inversion of an n x n covariance matrix. Approximating the model with a GMRF defined on an N x N lattice, the computations can be reduced to inversion of an NxN band limited matrix. For large data sets the full <br/><br> n x n matrix might not be possible to invert, and the GMRF approximation is then not only time saving, but is what makes it possible to perform kriging with the full data set.}, author = {Werner Hartman, Linda}, language = {eng}, note = {Licentiate Thesis}, title = {Spatial inference for nonlattice data using Markov Random fields}, year = {2004}, }