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dc.contributor.authorBakka, Haakon
dc.contributor.authorVanhatalo, Jarno
dc.contributor.authorIllian, Janine B.
dc.contributor.authorSimpson, Daniel
dc.contributor.authorRue, Haavard
dc.date.accessioned2020-01-18T00:34:47Z
dc.date.available2020-01-18T00:34:47Z
dc.date.issued2019-01-18
dc.identifier.citationBakka , H , Vanhatalo , J , Illian , J B , Simpson , D & Rue , H 2019 , ' Non-stationary Gaussian models with physical barriers ' , Spatial Statistics , vol. In press . https://doi.org/10.1016/j.spasta.2019.01.002en
dc.identifier.issn2211-6753
dc.identifier.otherPURE: 257463684
dc.identifier.otherPURE UUID: 5baea21e-a264-4ca5-8fcf-6506e2c1906a
dc.identifier.otherRIS: urn:860E81DC76368D30E0C4659EDDBE58EE
dc.identifier.otherScopus: 85060491682
dc.identifier.otherWOS: 000460136700015
dc.identifier.urihttps://hdl.handle.net/10023/19307
dc.descriptionData collection was funded by VELMU and the Natural Resources Institute Finland (Luke).en
dc.description.abstractThe classical tools in spatial statistics are stationary models, like the Matérn field. However, in some applications there are boundaries, holes, or physical barriers in the study area, e.g. a coastline, and stationary models will inappropriately smooth over these features, requiring the use of a non-stationary model. We propose a new model, the Barrier model, which is different from the established methods as it is not based on the shortest distance around the physical barrier, nor on boundary conditions. The Barrier model is based on viewing the Matérn correlation, not as a correlation function on the shortest distance between two points, but as a collection of paths through a Simultaneous Autoregressive (SAR) model. We then manipulate these local dependencies to cut off paths that are crossing the physical barriers. To make the new SAR well behaved, we formulate it as a stochastic partial differential equation (SPDE) that can be discretised to represent the Gaussian field, with a sparse precision matrix that is automatically positive definite. The main advantage with the Barrier model is that the computational cost is the same as for the stationary model. The model is easy to use, and can deal with both sparse data and very complex barriers, as shown in an application in the Finnish Archipelago Sea. Additionally, the Barrier model is better at reconstructing the modified Horseshoe test function than the standard models used in R-INLA.
dc.language.isoeng
dc.relation.ispartofSpatial Statisticsen
dc.rightsCopyright © 2019 Elsevier B.V. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.spasta.2019.01.002en
dc.subjectArchipelagoen
dc.subjectBarriersen
dc.subjectCoastline problemen
dc.subjectINLAen
dc.subjectSpatial statisticsen
dc.subjectStochastic partial differential equationsen
dc.subjectQA Mathematicsen
dc.subjectNDASen
dc.subject.lccQAen
dc.titleNon-stationary Gaussian models with physical barriersen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Scottish Oceans Instituteen
dc.contributor.institutionUniversity of St Andrews. Centre for Research into Ecological & Environmental Modellingen
dc.identifier.doihttps://doi.org/10.1016/j.spasta.2019.01.002
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-01-18


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