Advanced

Bayesian modelling of spatial data using Markov random fields, with application to elemental composition of forest soil

Werner Hartman, Linda LU (2006) In Mathematical Geology 38(2). p.113-133
Abstract
Spatial datasets are common in the environmental sciences. In this study we suggest a hierarchical model for a spatial stochastic field. The main focus of this article is to approximate a stochastic field with a Gaussian Markov Random Field (GMRF) to exploit computational advantages of the Markov field, concerning predictions, etc. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a GMRF defined on a lattice. To estimate model parameters we adopt a Bayesian perspective, and use Monte Carlo integration with samples from Markov Chain simulations. Our methods does not demand lattice, or near-lattice data, but are developed for a general spatial data-set, leaving the lattice to be specified... (More)
Spatial datasets are common in the environmental sciences. In this study we suggest a hierarchical model for a spatial stochastic field. The main focus of this article is to approximate a stochastic field with a Gaussian Markov Random Field (GMRF) to exploit computational advantages of the Markov field, concerning predictions, etc. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a GMRF defined on a lattice. To estimate model parameters we adopt a Bayesian perspective, and use Monte Carlo integration with samples from Markov Chain simulations. Our methods does not demand lattice, or near-lattice data, but are developed for a general spatial data-set, leaving the lattice to be specified by the modeller. The model selection problem that comes with the artificial grid is in this article addressed with cross-validation, but we also suggest other alternatives. From the application of the methods to a data set of elemental composition of forest soil, we obtained predictive distributions at arbitrary locations as well as estimates of model parameters. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
nonlattice, Gaussian Markov random field, Markov chain Monte Carlo, data, bilinear interpolation
in
Mathematical Geology
volume
38
issue
2
pages
113 - 133
publisher
Springer
external identifiers
  • wos:000238532700002
  • scopus:33745299514
ISSN
0882-8121
DOI
10.1007/s11004-005-9009-5
language
English
LU publication?
yes
id
9f5a515e-a0e0-4616-a842-933b8ab5190d (old id 404829)
date added to LUP
2016-04-01 16:17:31
date last changed
2019-11-20 03:36:03
@article{9f5a515e-a0e0-4616-a842-933b8ab5190d,
  abstract     = {Spatial datasets are common in the environmental sciences. In this study we suggest a hierarchical model for a spatial stochastic field. The main focus of this article is to approximate a stochastic field with a Gaussian Markov Random Field (GMRF) to exploit computational advantages of the Markov field, concerning predictions, etc. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a GMRF defined on a lattice. To estimate model parameters we adopt a Bayesian perspective, and use Monte Carlo integration with samples from Markov Chain simulations. Our methods does not demand lattice, or near-lattice data, but are developed for a general spatial data-set, leaving the lattice to be specified by the modeller. The model selection problem that comes with the artificial grid is in this article addressed with cross-validation, but we also suggest other alternatives. From the application of the methods to a data set of elemental composition of forest soil, we obtained predictive distributions at arbitrary locations as well as estimates of model parameters.},
  author       = {Werner Hartman, Linda},
  issn         = {0882-8121},
  language     = {eng},
  number       = {2},
  pages        = {113--133},
  publisher    = {Springer},
  series       = {Mathematical Geology},
  title        = {Bayesian modelling of spatial data using Markov random fields, with application to elemental composition of forest soil},
  url          = {http://dx.doi.org/10.1007/s11004-005-9009-5},
  doi          = {10.1007/s11004-005-9009-5},
  volume       = {38},
  year         = {2006},
}