Multivariate type G Matérn stochastic partial differential equation random fields
(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
- Bolin, David LU and Wallin, Jonas LU
- organization
- publishing date
- 2020-02
- 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
- 2022-04-18 19:49:19
@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}},
keywords = {{Matérn covariances; Multivariate random fields; Non-Gaussian models; Spatial statistics; Stochastic partial differential equations}},
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}},
}