CrossValidationMuFicokm: Cross Validation Procedure for Multi-Fidelity Cokriging models when the observations are removed from the code with the highest level of fidelity

Description

Provide the predictive errors and variances of a cross validation procedure when observations (not necessarily one) are removed only from the code with the highest level of fidelity.

Usage

CrossValidationMuFicokm(model, indice)

Arguments

model

an object of class S3 ("MuFicokm") provided by the function "MuFicokm" corresponding to the multi-fidelity cokriging model.

indice

a vector containing the indices of the observations removed from the highest code level for the cross-validation procedure.

Value

CVerr: a vector containing the predictive errors of the cross-validation procedure.
CVvar: a vector containing the predictive variances of the cross-validation procedure.
CVCov: a matrix representing the predictive covariance matrix of the cross-validation procedure.

References

DUBRULE, O. (1983), Cross Validation in a Unique Neightborhood. Mathematical Geology 15. Mo.6

ZHANG, H. and WANG, Y. (2009), Kriging and cross-validation for massive spatial data. Environmetrics 21, 290-304.

LE GRATIET, L. & GARNIER, J. (2012), Recursive co-kriging model for Design of Computer Experiments with multiple levels of fidelity, arXiv:1210.0686

Examples

Run this code

#--- test functions (see [Le GRATIET, L. 2012])
	Funcf <- function(x){return(0.5*(6*x-2)^2*sin(12*x-4)+sin(10*cos(5*x)))}
	Funcc <- function(x){return((6*x-2)^2*sin(12*x-4)+10*(x-0.5)-5)}
#--- Data
	Dc <- seq(0,1,0.1)
	indDf <- c(1,3,7,11)
	DNest <- NestedDesign(Dc, nlevel=2 , indices = list(indDf) )
	zc <- Funcc(DNest$PX)
	zf <- Funcf(ExtractNestDesign(DNest,2))

#--- Model creation
		mymodel <- MuFicokm(
				formula = list(~1,~1+X1), 
				MuFidesign = DNest, 
				response = list(zc,zf), 
				nlevel = 2,
				covtype = "matern5_2")
#--- Cross Validation on points number  1 and 3
		indice <- c(1,3)
		CrossValidationMuFicokm(mymodel,indice)
#--- Leave-One-Out Cross Validation
	#-- LOO CV predictive errors
		apply(matrix(1:DNest$n),1,function(x) CrossValidationMuFicokm(mymodel,x)$CVerr)
	#-- LOO CV predictive variances
		apply(matrix(1:DNest$n),1,function(x) CrossValidationMuFicokm(mymodel,x)$CVvar)