Non-stationary Gaussian models with physical barriers
| Autor: | Haakon Bakka, Jarno Vanhatalo, Janine B. Illian, Daniel Simpson, Haavard Rue |
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| Přispěvatelé: | Department of Mathematics and Statistics, Organismal and Evolutionary Biology Research Programme, Research Centre for Ecological Change, Environmental and Ecological Statistics Group, Biostatistics Helsinki, University of St Andrews. Statistics, University of St Andrews. Scottish Oceans Institute, University of St Andrews. Centre for Research into Ecological & Environmental Modelling |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
AFRICA 1171 Geosciences 0106 biological sciences Statistics and Probability Computer science Gaussian NDAS Coastline problem Management Monitoring Policy and Law Correlation function (astronomy) Statistics - Applications 01 natural sciences Methodology (stat.ME) 010104 statistics & probability symbols.namesake INLA Applied mathematics Applications (stat.AP) QA Mathematics Boundary value problem 0101 mathematics Computers in Earth Sciences QA Spatial analysis Statistics - Methodology Sparse matrix Archipelago Spatial statistics PLASMODIUM-FALCIPARUM 010604 marine biology & hydrobiology Stochastic partial differential equations Stochastic partial differential equation Autoregressive model symbols Test functions for optimization Barriers |
| Zdroj: | Spatial Statistics. 29:268-288 |
| ISSN: | 2211-6753 |
| DOI: | 10.1016/j.spasta.2019.01.002 |
| Popis: | The classical tools in spatial statistics are stationary models, like the Mat\'ern 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 Mat\'ern 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. Comment: The new version contains major changes and new materials, including a much more appropriate proof of existence of solution to the SPDE |
| Databáze: | OpenAIRE |
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