LatticeKrig (version 8.4)
Multi-Resolution Kriging Based on Markov Random Fields
Description
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.