GeoKrigloc: Spatial (bivariate) and spatio temporal optimal linear local...

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

Spatial (bivariate) and spatio temporal optimal linear local prediction for Gaussian and non-Gaussian random fields.

Description

For a given set of spatial location sites (and temporal instants), the function computes optmal local linear prediction and the associated mean squared error for the Gaussian and non-Gaussian case using a spatial (temporal) neighborhood computed using the function GeoNeighborhood

Usage

GeoKrigloc(estobj=NULL,data, 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, mse=FALSE, 
 param, anisopars=NULL,radius=1,
 sparse=FALSE, time=NULL, type="Standard",
 type_krig="Simple",weigthed=TRUE, 
 which=1, copula=NULL,X=NULL,Xloc=NULL,Mloc=NULL,varcov=NULL,
 spobj=NULL,spdata=NULL,parallel=FALSE,ncores=NULL,progress=TRUE)

Arguments

estobj	An object of class Geofit that includes information about data, model and estimates.
data	A d-dimensional vector (a single spatial realisation) or a (d \times d)-matrix (a single spatial realisation on regular grid) or a (t \times d)-matrix (a single spatio-temporal realisation) or an (d \times d \times t \times n )-array (a single spatio-temporal realisation on regular grid) giving the data used for prediction.
coordx	A numeric (d \times 2)-matrix or (d \times 3)-matrix Coordinates on a sphere for a fixed radius radius are passed in lon/lat format expressed in decimal degrees.
coordy	A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.
coordz	A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.
coordt	A numeric vector giving 1-dimension of temporal coordinates used for prediction; the default is NULL then a spatial random field is expected.
coordx_dyn	A list of m numeric (d_t \times 2)-matrices containing dynamical (in time) spatial coordinates. Optional argument, the default is NULL
corrmodel	String; the name of a correlation model, for the see GeoCovmatrix for the list of implemented correlation models.
distance	String; the name of the spatial distance. The default is Eucl, the Euclidean distance. See GeoFit for details.
grid	Logical; if FALSE (the default) the data used for prediction are interpreted as spatial or spatio-temporal realisations on a set of non-equispaced spatial sites (irregular grid).
loc	A numeric (n \times 2)-matrix (where n is the number of spatial sites) giving 2-dimensions of spatial coordinates to be predicted.
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	String; the type of matrix decomposition used in the simulation. Default is cholesky. The other possible choices is svd.
n	Numeric; the number of trials in a binomial random fields. Default is 1.
nloc	Numeric; the number of trials of the locations sites to be predicted in the binomial random field. If missing then a rounded mean of n is considered.
mse	Logical; if TRUE (the default) MSE of the kriging predictor is computed
model	String; the type of RF and therefore the densities associated to the likelihood objects. Gaussian is the default, see the Section Details.
param	A list of parameter values required for the correlation model. See Details for the accepted options.
anisopars	A list of two elements: "angle" and "ratio" i.e. the anisotropy angle and the anisotropy ratio, respectively.
radius	Numeric: the radius of the sphere if coordinates are passed in lon/lat format;Default value is 1.
sparse	Logical; if TRUE kriging is computed with sparse matrices algorithms using spam package. Default is FALSE. It should be used with compactly supported covariances.
time	A numeric (m \times 1) vector (where m is the number of temporal instants) giving the temporal instants to be predicted; the default is NULL then only spatial prediction is performed.
type	String; if Standard then standard kriging is performed;if Tapering then kriging with covariance tapering is performed;if Pairwise then pairwise kriging is performed
type_krig	String; the type of kriging. If Simple (the default) then simple kriging is performed. Otherwise Universal
weigthed	Logical; if TRUE then decreasing weigths coming from a compactly supported correlation function with compact support maxdist (maxtime)are used in the pairwise kriging.
which	Numeric; In the case of bivariate (tapered) cokriging it indicates which variable to predict. It can be 1 or 2
copula	String; the type of copula. It can be "Clayton" or "Gaussian"
X	Numeric; Matrix of spatio(temporal)covariates in the linear mean specification.
Xloc	Numeric; Matrix of spatio(temporal)covariates in the linear mean specification associated to predicted locations.
Mloc	Numeric; Vector of spatio(temporal) estimated means associated to predicted locations.
varcov	Inverse of the covariance matrix estimates.
spobj	An object of class sp or spacetime
spdata	Character:The name of data in the sp or spacetime object
parallel	Logical; if TRUE then the prediction computation is parallelized
ncores	Numeric; number of cores involved in parallelization.
progress	If TRUE then a progress bar is shown.

Details

This function use the GeoKrig with a spatial or spatio-temporal neighborhood computed using the function GeoNeighborhood. The neighborhood is specified with the option maxdist and maxtime.

Value

Returns an object of class Kg. An object of class Kg is a list containing at most the following components:

bivariate	TRUE if spatial bivariate cokriging is performed, otherwise FALSE;
coordx	A d-dimensional vector of spatial coordinates used for prediction;
coordy	A d-dimensional vector of spatial coordinates used for prediction;
coordz	A d-dimensional vector of spatial coordinates used for prediction;
coordt	A t-dimensional vector of temporal coordinates used for prediction;
corrmodel	String: the correlation model;
covmatrix	The covariance matrix if type is Standard. An object of class spam if type is Tapering
data	The vector or matrix or array of data used for prediction
distance	String: the type of spatial distance;
grid	TRUE if the spatial data used for prediction are observed in a regular grid, otherwise FALSE;
loc	A (n \times 2)-matrix of spatial locations to be predicted.
n	The number of trial for Binomial random fields
nozero	In the case of tapered simple kriging the percentage of non zero values in the covariance matrix. Otherwise is NULL.
numcoord	Numeric:he number d of spatial coordinates used for prediction;
numloc	Numeric: the number n of spatial coordinates to be predicted;
numtime	Numeric: the number d of the temporal instants used for prediction;
numt	Numeric: the number m of the temporal instants to be predicted;
model	The type of RF, see GeoFit.
param	Numeric: The covariance parameters;
pred	A (m \times n)-matrix of spatio or spatio temporal kriging prediction;
radius	Numeric: the radius of the sphere if coordinates are pssed in lon/lat format;
spacetime	TRUE if spatio-temporal kriging and FALSE if spatial kriging;
tapmod	String: the taper model if type is Tapering. Otherwise is NULL.
time	A m-dimensional vector of temporal coordinates to be predicted;
type	String: the type of kriging (Standard or Tapering).
type_krig	String: the type of kriging: Simple or Universal
mse	A (m \times n)-matrix of spatio or spatio temporal mean square error kriging prediction;

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

References

Gaetan, C. and Guyon, X. (2010) Spatial Statistics and Modelling. Springer-Verlag, New York. Furrer R., Genton, M.G. and Nychka D. (2006). Covariance Tapering for Interpolation of Large Spatial Datasets. Journal of Computational and Graphical Statistics, 15-3, 502–523.

See Also

GeoCovmatrix

Examples

################################################################
############### Examples of Spatial local kriging #############
################################################################
require(GeoModels)
####
model="Gaussian"

# Define the spatial-coordinates of the points:
set.seed(759)
x = runif(1000, 0, 1)
y = runif(1000, 0, 1)
coords=cbind(x,y)
# Set the exponential cov parameters:
corrmodel = "GenWend"
mean=0; sill=1
nugget=0; scale=0.2
param=list(mean=mean,sill=sill,nugget=nugget,smooth=0,
scale=scale,power2=4)

# Simulation of the spatial Gaussian random field:
data = GeoSim(coordx=coords, corrmodel=corrmodel,
 param=param)$data

# Maximum pairwise likelihood fitting of the space time random field:

start=list(scale=scale,sill=sill,mean=mean)
fixed=list(power2=4,smooth=0,nugget=0)
fit = GeoFit(data, coordx=coords, corrmodel=corrmodel, 
 start=start,fixed=fixed,
 likelihood='Conditional', type='Pairwise',
 neighb=3)

# locations to predict
loc_to_pred=matrix(runif(8),4,2)
################################################################
###
### Example 1. Comparing spatial kriging with local kriging for
### a Gaussian random field with GenWend correlation.
### 
###############################################################
param=append(fit$param,fit$fixed)
pr=GeoKrig(fit,loc=loc_to_pred,mse=TRUE)

pr_loc=GeoKrigloc(fit,loc=loc_to_pred,neighb=100,mse=TRUE)

pr$pred;
pr_loc$pred


############################################################
#### Example: spatio temporal Gaussian local kriging ######
############################################################


require(GeoModels)
require(fields)
set.seed(78)
coords=cbind(runif(100),runif(100))
coordt=seq(0,5,0.25)
corrmodel="Matern_Matern"
param=list(nugget=0,mean=0,scale_s=0.2/3,scale_t=0.25/3,sill=2,
 smooth_s=0.5,smooth_t=0.5)

data = GeoSim(coordx=coords, coordt=coordt,
 corrmodel=corrmodel, param=param)$data


# Maximum pairwise likelihood fitting of the space time random field:
start = list(scale_s=0.2/3,scale_t=0.25,sill=2,mean=0)
fixed = list(smooth_s=0.5,smooth_t=0.5,nugget=0)
I=Inf
lower=list(scale_s=0,scale_t=0,sill=0,mean=-I)
upper=list(scale_s=I,scale_t=I,sill=I,mean=I)
fit = GeoFit(data, coordx=coords, coordt=coordt, model=model, corrmodel=corrmodel, 
 likelihood='Conditional', type='Pairwise',start=start,fixed=fixed,
 optimizer="nlminb",lower=lower,upper=upper,
 neighb=3,maxtime=1)

## four location to predict
loc_to_pred=matrix(runif(8),4,2)
## three temporal instants to predict
time=c(0.5,1.5,3.5)


pr=GeoKrig(fit,loc=loc_to_pred,time=time,mse=TRUE)
pr_loc=GeoKrigloc(fit,loc=loc_to_pred,time=time,
 neigh=25,maxtime=1, mse=TRUE)

## full and local prediction 
pr$pred
pr_loc$pred



############################################################
#### Example: spatio bivariate Gaussian local cokriging ######
############################################################
#set.seed(6)
#NN=1500 # number of spatial locations 
#x = runif(NN, 0, 1); 
#y = runif(NN, 0, 1) 
#coords=cbind(x,y) 

## setting parameters
#mean_1 = 2; mean_2= -1
#nugget_1 =0;nugget_2=0
#sill_1 =0.5; sill_2 =1; 

### correlation parameters
#CorrParam("Bi_Matern")
#scale_1=0.2/3; scale_2=0.15/3; scale_12=0.5*(scale_2+scale_1) 
#smooth_1=smooth_2=smooth_12=0.5
#pcol = -0.4
#param= list(nugget_1=nugget_1,nugget_2=nugget_2,
# sill_1=sill_1,sill_2=sill_2,
# mean_1=mean_1,mean_2=mean_2,
# smooth_1=smooth_1, smooth_2=smooth_2,smooth_12=smooth_12,
# scale_1=scale_1, scale_2=scale_2,scale_12=scale_12,
# pcol=pcol)

## simulation
#data = GeoSim(coordx=coords, corrmodel="Bi_Matern",model=model,param=param)$data

#fixed=list(mean_1=mean_1,mean_2=mean_2, nugget_1=nugget_1,nugget_2=nugget_2, 
# smooth_1=smooth_1, smooth_2=smooth_2,smooth_12=smooth_12)

#start=list( sill_1=sill_1,sill_2=sill_2,
# scale_1=scale_1,scale_2=scale_2,scale_12=scale_12, pcol=pcol)

## estimation with maximum likelihood 
#fit = GeoFit(data=data,coordx=coords, corrmodel="Bi_Matern",
 # likelihood="Marginal",type="Pairwise",optimizer="BFGS",neighb=5,
 #start=start,fixed=fixed)

###### co-kriging for the fist component ##############
#xx=seq(0,1,0.022)
#loc_to_pred=as.matrix(expand.grid(xx,xx))
#pr1 = GeoKrigloc(fit,which=1,mse=TRUE,loc=loc_to_pred,neighb=100)

#opar=par(no.readonly = TRUE)
#par(mfrow=c(1,2))
#zlim=c(-2.5,2.5)
#colour = rainbow(100)
#quilt.plot(coords,data[1,] ,col=colour,main = paste(" Fist component")) 
#quilt.plot(loc_to_pred,pr1$pred,col=colour,
# main = paste(" Kriging first component"),ylab="")
#par(opar)

GeoModels documentation built on July 29, 2026, 5:06 p.m.