GeoKriglocWeights: Compute kriging weights (and related quantities) for Gaussian...

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

Compute kriging weights (and related quantities) for Gaussian / non-Gaussian spatial, spatio-temporal or multivariate random fields

Description

Given a set of spatial locations (and possibly temporal instants) the function returns the vector (or matrix) of kriging weights, the covariance matrix used in the kriging system and, optionally, the inverse of the left-hand-side matrix dor a specified neighborhhod

Usage

GeoKriglocWeights(coordx, coordy=NULL, coordz=NULL, coordt=NULL, coordx_dyn=NULL,
 corrmodel, distance="Eucl", grid=FALSE, loc, neighb=NULL,
 maxdist=NULL, maxtime=NULL, method="cholesky", model="Gaussian",
 n=1, nloc=NULL, param, anisopars=NULL,
 radius=1, sparse=FALSE, time=NULL, which=1,
 copula=NULL, X=NULL, Xloc=NULL, Mloc=NULL,parallel=TRUE)

Arguments

coordx	Numeric (d\times 2) or (d\times 3) matrix of spatial coordinates. Coordinates on a sphere are accepted (lon/lat in decimal degrees) when distance = "Sphere".
coordy	Optional numeric vector giving an additional spatial coordinate dimension. Ignored if coordx is already a matrix.
coordz	Optional numeric vector giving a third spatial coordinate dimension.
coordt	Optional numeric vector of temporal coordinates (length t). If missing, a purely spatial random field is assumed.
coordx_dyn	List of m matrices (d_t\times 2) containing time-varying spatial coordinates. See GeoKrig.
corrmodel	Character string naming a valid correlation model. See GeoCovmatrix for admissible choices.
distance	Character string specifying the spatial distance. Default is "Eucl" (Euclidean). See GeoFit.
grid	Logical. If TRUE, coordinates are interpreted as defining a regular grid (see GeoKrig).
loc	Numeric (n\times 2) matrix of locations for which the kriging weights are required.
neighb	Numeric; an optional positive integer indicating the order of the neighborhood.
maxdist	Numeric; an optional positive value indicating the distance in the spatial neighborhood.
maxtime	Numeric; an optional positive integer value indicating the order of the temporal neighborhood.
method	Character string indicating the matrix factorisation used to solve the kriging system: "cholesky" (default) or "svd".
model	Character string specifying the random field type (e.g.\ "Gaussian", "SkewGaussian", "Gamma", …). See GeoFit.
n	Integer. Number of trials for Binomial random fields (default 1).
nloc	Integer. Number of trials for the prediction locations in Binomial random fields (default 1).
param	Named list of covariance and mean parameters. See CorrParam and GeoCovmatrix.
anisopars	List with components angle and ratio defining geometric anisotropy (optional).
radius	Positive numeric value: sphere radius when coordinates are lon/lat (default 1).
sparse	Logical. If TRUE, sparse‐matrix algorithms (package spam) are employed. Only effective with compactly supported covariance functions.
time	Numeric vector of length m giving the temporal instants for which weights are required. Ignored if coordt is missing.
which	Integer (1 or 2) selecting the variable whose weights are returned in the bivariate case.
copula	Character string naming a copula when a non-Gaussian dependence structure is used ("Clayton" or "Gaussian").
X	Numeric matrix of spatio-temporal covariates at data locations.
Xloc	Numeric matrix of spatio-temporal covariates at prediction locations.
Mloc	Numeric; Vector of spatio(temporal) estimated means associated to predicted locations.
parallel	Logical; if TRUE then parallelization is performed

Details

The function builds the kriging system

\Sigma \mathbf{w} = \boldsymbol{\sigma}_0

where \Sigma is the covariance matrix between observed locations and \boldsymbol{\sigma}_0 the vector of covariances between observed and prediction locations. The solution \mathbf{w} is returned together with \Sigma and, optionally, \Sigma^{-1}. Universal kriging with covariates is supported; in that case the generalised least squares estimate of the mean parameters is appended. No actual prediction is carried out; for full kriging use GeoKrig.

Value

An object of class KgWeights, a list containing:

weights	Numeric vector (or matrix) of kriging weights.
covmat	Covariance matrix \Sigma used in the kriging system.
invcov	Inverse of \Sigma (only if sparse = FALSE).
beta	Estimated regression coefficients when covariates are supplied.
type	Character string: "simple" or "universal".
model	Input model.
corrmodel	Input corrmodel.
spacetime	Logical: TRUE for spatio-temporal case, FALSE otherwise.
sparse	Logical: was a sparse algorithm used?
loc	Copy of the loc argument.
time	Copy of the time argument (if any).

Author(s)

Moreno Bevilacqua, [e-mail], Víctor Morales-Oñate, [e-mail], Christian Caamaño-Carrillo, [e-mail]

References

Gaetan, C. and Guyon, X. (2010) Spatial Statistics and Modeling. Springer-Verlag, New York.

See Also

GeoKrig for full prediction, GeoKrigloc for local prediction, GeoCovmatrix for covariance model details,

GeoModels documentation built on Sept. 1, 2025, 1:09 a.m.