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Latent Gaussian random field mixture models

Wallin, Jonas LU ; Bolin, David and Lindgren, Finn (2018) In Computational Statistics and Data Analysis 130. p.80-93
Abstract
For many problems in geostatistics, land cover classification, and brain imaging the classical Gaussian process models are unsuitable due to sudden, discontinuous, changes in the data. To handle data of this type, we introduce a new model class that combines discrete Markov random fields (MRFs) with Gaussian Markov random fields. The model is defined as a mixture of several, possibly multivariate, Gaussian Markov random fields. For each spatial location, the discrete MRF determines which of the Gaussian fields in the mixture that is observed. This allows for the desired discontinuous changes of the latent processes, and also gives a probabilistic representation of where the changes occur spatially. By combining stochastic gradient... (More)
For many problems in geostatistics, land cover classification, and brain imaging the classical Gaussian process models are unsuitable due to sudden, discontinuous, changes in the data. To handle data of this type, we introduce a new model class that combines discrete Markov random fields (MRFs) with Gaussian Markov random fields. The model is defined as a mixture of several, possibly multivariate, Gaussian Markov random fields. For each spatial location, the discrete MRF determines which of the Gaussian fields in the mixture that is observed. This allows for the desired discontinuous changes of the latent processes, and also gives a probabilistic representation of where the changes occur spatially. By combining stochastic gradient minimization with sparse matrix techniques we obtain computationally efficient methods for both likelihood-based parameter estimation and spatial interpolation. The model is compared to Gaussian models and standard MRF models using simulated data and in application to upscaling of soil permeability data. (Less)
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Computational Statistics and Data Analysis
volume
130
pages
80 - 93
publisher
Elsevier
external identifiers
  • scopus:85053763129
ISSN
0167-9473
DOI
10.1016/j.csda.2018.08.007
language
English
LU publication?
yes
id
66e74238-157c-49db-84f3-c8a354310684
date added to LUP
2017-12-20 08:53:17
date last changed
2022-04-25 04:29:44
@article{66e74238-157c-49db-84f3-c8a354310684,
  abstract     = {{For many problems in geostatistics, land cover classification, and brain imaging the classical Gaussian process models are unsuitable due to sudden, discontinuous, changes in the data. To handle data of this type, we introduce a new model class that combines discrete Markov random fields (MRFs) with Gaussian Markov random fields. The model is defined as a mixture of several, possibly multivariate, Gaussian Markov random fields. For each spatial location, the discrete MRF determines which of the Gaussian fields in the mixture that is observed. This allows for the desired discontinuous changes of the latent processes, and also gives a probabilistic representation of where the changes occur spatially. By combining stochastic gradient minimization with sparse matrix techniques we obtain computationally efficient methods for both likelihood-based parameter estimation and spatial interpolation. The model is compared to Gaussian models and standard MRF models using simulated data and in application to upscaling of soil permeability data.}},
  author       = {{Wallin, Jonas and Bolin, David and Lindgren, Finn}},
  issn         = {{0167-9473}},
  language     = {{eng}},
  pages        = {{80--93}},
  publisher    = {{Elsevier}},
  series       = {{Computational Statistics and Data Analysis}},
  title        = {{Latent Gaussian random field mixture models}},
  url          = {{http://dx.doi.org/10.1016/j.csda.2018.08.007}},
  doi          = {{10.1016/j.csda.2018.08.007}},
  volume       = {{130}},
  year         = {{2018}},
}