Description Usage Arguments Value Author(s) References See Also Examples
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.
1 | CrossValidationMuFicokm(model, indice)
|
model |
an object of class S3 ( |
indice |
a vector containing the indices of the observations removed from the highest code level for the cross-validation procedure. |
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. |
Loic Le Gratiet
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
MuFicokm
, CrossValidationMuFicokmAll
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | #--- 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)
|
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
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