CrossValidationMuFicokm: Cross Validation Procedure for Multi-Fidelity Cokriging...

In MuFiCokriging: Multi-Fidelity Cokriging models

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.

Author(s)

Loic Le Gratiet

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

See Also

MuFicokm, CrossValidationMuFicokmAll

Examples

#--- 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)

Example output

Loading required package: DiceKriging

optimisation start
------------------
* estimation method   : MLE 
* optimisation method : BFGS 
* analytical gradient : used
* trend model : ~1
* covariance model : 
  - type :  matern5_2 
  - nugget : NO
  - parameters lower bounds :  1e-10 
  - parameters upper bounds :  2 
  - best initial criterion value(s) :  -30.12602 

N = 1, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate     0  f=       30.126  |proj g|=       1.7326
At iterate     1  f =       30.034  |proj g|=       0.30499
At iterate     2  f =       30.033  |proj g|=      0.071705
At iterate     3  f =       30.033  |proj g|=     0.0012044
At iterate     4  f =       30.033  |proj g|=    2.7838e-06

iterations 4
function evaluations 7
segments explored during Cauchy searches 4
BFGS updates skipped 0
active bounds at final generalized Cauchy point 0
norm of the final projected gradient 2.7838e-06
final function value 30.0335

F = 30.0335
final  value 30.033468 
converged

optimisation start
------------------
* estimation method   : MLE 
* optimisation method : BFGS 
* analytical gradient : used
* trend model : ~X1
* covariance model : 
  - type :  matern5_2 
  - nugget : NO
  - parameters lower bounds :  1e-10 
  - parameters upper bounds :  2 
  - best initial criterion value(s) :  -0.9792429 

N = 1, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate     0  f=      0.97924  |proj g|=      0.15881
At iterate     1  f =      0.32578  |proj g|=             0

iterations 1
function evaluations 2
segments explored during Cauchy searches 1
BFGS updates skipped 0
active bounds at final generalized Cauchy point 1
norm of the final projected gradient 0
final function value 0.32578

F = 0.32578
final  value 0.325780 
converged
$CVerr
[1] 0.2314433 0.2326346

$CVvar
[1] 0.0689077 0.0689077

$CVCov
          [,1]      [,2]
[1,] 0.0689077 0.0000000
[2,] 0.0000000 0.0689077

[1]  0.23144334 -0.40562147  0.23263461 -0.05845647
[1] 0.0689077 0.0689077 0.0689077 0.0689077

MuFiCokriging documentation built on May 2, 2019, 3:33 p.m.