Non-stationary Gaussian models with physical barriers
Abstract
The 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.
Citation
Bakka , 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.2019.01.002
Publication
Spatial Statistics
Status
Peer reviewed
ISSN
2211-6753Type
Journal article
Rights
Copyright © 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.2019.01.002
Description
Data collection was funded by VELMU and the Natural Resources Institute Finland (Luke).Collections
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