LatticeKrig: Multiresolution Kriging Based on Markov Random Fields

Methods for the interpolation of large spatial datasets. This package follows a "fixed rank Kriging" approach using a large number of basis functions and provides spatial estimates that are comparable to standard families of covariance functions. 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 this. 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 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.

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