Multi-Resolution Kriging Based on Markov Random Fields // Methods
for the interpolation of large spatial datasets. This package
follows a "fixed rank Kriging" approach but provides a surface
fitting method that can approximate standard spatial data
models. Using a large number of basis functions allows for
estimates that can come close to interpolating the observations
(a spatial model with a small nugget variance.) Moreover, the
covariance model for this method can approximate the Matern
covariance family but also allows for a multi-resolution model
and supports efficient computation of the profile likelihood
for estimating covariance parameters. This is accomplished
through compactly supported basis functions and a Markov random
field model for the basis coefficients. These features lead to
sparse matrices for the computations and this package makes of
the R spam package for sparse linear algebra. An extension of
this version over previous ones ( 5.4 ) is the support for
different geometries besides a rectangular domain. The Markov
random field approach combined with a basis function
representation makes the implementation of different geometries
simple where only a few specific R functions need to be added
with most of the computation and evaluation done by generic
routines that have been tuned to be efficient. One benefit of
this package's model/approach is the facility to do
unconditional and conditional simulation of the field for large
numbers of arbitrary points. There is also the flexibility for
estimating non-stationary covariances and also the case when
the observations are a linear combination (e.g. an integral) of
the spatial process. Included are generic methods for
prediction, standard errors for prediction, plotting of the
estimated surface and conditional and unconditional simulation.
See the 'LatticeKrig' GitHub repository for a vignette of this
package. Development of this package was supported in part by
the National Science Foundation Grant 1417857 and the National
Center for Atmospheric Research.