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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