Thursday 14 Nov 2013Spatial methods that combine ideas from wavelets and lattices (joint with CliMathNet)

Doug Nychka - NCAR, USA

Harrison 103 15:00-16:00

Kriging is a non-parametric regression method used in geostatistics for estimating curves and surfaces and forms the core of most statistical methods for spatial data. In climate science these methods are very useful for estimating how climate varies over a geographic region when the observational data is sparse or the computer model runs are limited. A statistical challenge is to implement spatial methods for large sample sizes, a common feature of many geophysical
problems. Here a new family of covariance models is proposed that expands the field in a set of basis functions and places a Gaussian Markov random field (GMRF) latent model on the basis coefficients. The idea, in contrast to fixed rank Kriging, is to use many basis functions organized on lattices. In addition, the basis functions add more smoothness and larger scale spatial dependence that a GMRF alone. The computational efficiency arises because one can choose basis functions with compact support and also a precision matrix for the GMRF that is very sparse. The impact is that evaluating the model likelihood and computing spatial predictions is feasible even for tens of thousands of spatial observations. Moreover, by the varying the support of the basis functions and the correlations among basis coefficients it is possible to entertain multi-resolution and nonstationary spatial models. A practical example is also presented for a subset of the North American Regional Climate Change and Assessment Program model data. Here fields on the order 10^4 observations are compared within the R data analysis environment.

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