Show simple item record

dc.contributor.authorBakka, Haakon
dc.contributor.authorVanhatalo, Jarno
dc.contributor.authorIllian, Janine B.
dc.contributor.authorSimpson, Daniel
dc.contributor.authorRue, Haavard
dc.date.accessioned2019-02-20T07:04:23Z
dc.date.available2019-02-20T07:04:23Z
dc.date.issued2019-01-18
dc.identifier.citationBakka H, Vanhatalo J, Illian JB, Simpson D, Rue H (2019) Non-stationary Gaussian models with physical barriers. Spatial Statistics 29: 268–288. Available: http://dx.doi.org/10.1016/j.spasta.2019.01.002.
dc.identifier.issn2211-6753
dc.identifier.doi10.1016/j.spasta.2019.01.002
dc.identifier.urihttp://hdl.handle.net/10754/631094
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.description.sponsorshipWe are grateful to Simon Wood and Rosa Crujeiras Casais for detailed feedback on this research project, to Finn Lindgren for assistance with understanding the finer details of the SPDE approach, and to David Bolin for assistance with the theory of existence of solutions for SPDEs. Data collection was funded by VELMU and the Natural Resources Institute Finland (Luke). We appreciate the detailed feedback from reviewers.
dc.publisherElsevier BV
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S221167531830099X
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Spatial Statistics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Spatial Statistics, [29, , (2019-01-18)] DOI: 10.1016/j.spasta.2019.01.002 . © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectArchipelago
dc.subjectBarriers
dc.subjectCoastline problem
dc.subjectINLA
dc.subjectSpatial statistics
dc.subjectStochastic partial differential equations
dc.titleNon-stationary Gaussian models with physical barriers
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.identifier.journalSpatial Statistics
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Statistics, Faculty of Science, and Organismal and Evolutionary Biology Research Programme, Faculty of Bio- and Environmental Sciences, University of Helsinki, Gustaf Häströmin katu 2b, P.O. Box 68, FIN-00014 University of Helsinki, , Finland
dc.contributor.institutionCentre for Research into Ecological and Environmental Modelling, School of Mathematics and Statistics, University of St Andrews, The Observatory, Buchanan Gardens, St Andrews, Fife, Scotland, KY16 9LZ, , United Kingdom
dc.contributor.institutionDepartment of Statistical Sciences, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, , Canada
dc.identifier.arxivid1608.03787
kaust.personBakka, Haakon
kaust.personRue, Haavard
dc.date.published-online2019-01-18
dc.date.published-print2019-03


Files in this item

Thumbnail
Name:
1608.03787.pdf
Size:
6.359Mb
Format:
PDF
Description:
Accepted Manuscript

This item appears in the following Collection(s)

Show simple item record