KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2019-01-18
Print Publication Date2019-03
Permanent link to this recordhttp://hdl.handle.net/10754/631094
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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.
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.
SponsorsWe 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.