Non-linear optimal multivariate spatial design using spatial vine copulas
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A multivariate spatial sampling design that uses spatial vine copulas is presented that aims to simultaneously reduce the prediction uncertainty of multiple variables by selecting additional sampling locations based on the multivariate relationship between variables, the spatial configuration of existing locations and the values of the observations at those locations. Novel aspects of the methodology include the development of optimal designs that use spatial vine copulas to estimate prediction uncertainty and, additionally, use transformation methods for dimension reduction to model multivariate spatial dependence. Spatial vine copulas capture non-linear spatial dependence within variables, whilst a chained transformation that uses non-linear principal component analysis captures the non-linear multivariate dependence between variables. The proposed design methodology is applied to two environmental case studies. Performance of the proposed methodology is evaluated through partial redesigns of the original spatial designs. The first application is a soil contamination example that demonstrates the ability of the proposed methodology to address spatial non-linearity in the data. The second application is a forest biomass study that highlights the strength of the methodology in incorporating non-linear multivariate dependence into the design.
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|Item Type:||Journal Article|
|Keywords:||Adaptive sequential optimal design, Spatial sampling, Non-linear spatial dependence, Non-linear multivariate dependence, Spatial vine copula, Kriging|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)|
|Divisions:||Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2016 Springer-Verlag Berlin Heidelberg|
|Copyright Statement:||The final publication is available at Springer via http://dx.doi.org/10.1007/s00477-016-1307-6|
|Deposited On:||11 Sep 2016 23:40|
|Last Modified:||22 Oct 2016 08:01|
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