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Multivariate type G Matérn stochastic partial differential equation random fields

Bolin, David LU and Wallin, Jonas LU (2020) In Journal of the Royal Statistical Society. Series B: Statistical Methodology 82(1). p.215-239
Abstract

For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of... (More)

For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.

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author
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organization
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type
Contribution to journal
publication status
published
subject
keywords
Matérn covariances, Multivariate random fields, Non-Gaussian models, Spatial statistics, Stochastic partial differential equations
in
Journal of the Royal Statistical Society. Series B: Statistical Methodology
volume
82
issue
1
pages
25 pages
publisher
Wiley-Blackwell
external identifiers
  • scopus:85076726683
ISSN
1369-7412
DOI
10.1111/rssb.12351
language
English
LU publication?
yes
id
4c4a8e56-4e1f-4970-ac2e-cf0def8c1168
date added to LUP
2020-01-10 12:54:36
date last changed
2020-10-07 06:50:51
@article{4c4a8e56-4e1f-4970-ac2e-cf0def8c1168,
  abstract     = {<p>For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.</p>},
  author       = {Bolin, David and Wallin, Jonas},
  issn         = {1369-7412},
  language     = {eng},
  number       = {1},
  pages        = {215--239},
  publisher    = {Wiley-Blackwell},
  series       = {Journal of the Royal Statistical Society. Series B: Statistical Methodology},
  title        = {Multivariate type G Matérn stochastic partial differential equation random fields},
  url          = {http://dx.doi.org/10.1111/rssb.12351},
  doi          = {10.1111/rssb.12351},
  volume       = {82},
  year         = {2020},
}