MuFiCokriging (version 1.2)

summary.MuFicokm: Function summary for Multi-Fidelity Cokriging models

Description

Provide a summary of a multi-fidelity cokriging model. In particular, it provides the parameter estimations and the results of the cross-validation procedure.

Usage

"summary"(object, CrossValidation = FALSE, ...)

Arguments

object

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

CrossValidation

a Boolean. If TRUE, a Leave-One-Out cross validation procedure is performed. For the LOO procedure, the responses are removed from all code levels and the trend, adjustment and variance parameters are re-estimated after each removed observation.

...

no other argument for this method.

Value

A list with following items (see "MuFicokm"):

CovNames

a list of character strings giving the covariance structures used for the cokriging model. The element $i$ of the list corresponds to the covariance structure of the Gaussian process $\delta_i(x)$ with $\delta_1(x) = Z_1(x)$. (see "MuFicokm")

Cov.val

a list of vectors giving the values of the hyper-parameters of the cokriging model. The element $i$ of the list corresponds to the hyper-parameters of the Gaussian process $\delta_i(x)$ with $\delta_1(x) = Z_1(x)$. (see "MuFicokm")

Var.val

a list of numerics giving the values of the variance parameters of the cokriging model. The element $i$ of the list corresponds to the variance of the Gaussian process $\delta_i(x)$ with $\delta_1(x) = Z_1(x)$. (see "MuFicokm")

Rho.val

a list of vectors giving the values of the trends $\gamma_i$ of the adjustment parameters $\rho_i$ of the cokriging model. The element $i$ of the list corresponds to the adjustment parameter between $Z_i$ and $\delta_i(x)$. (see "MuFicokm")

Trend.val

a list of vectors giving the values of the trend parameters of the Gaussian processes $\delta_i(x)$ and $Z_1(x)$.

Details

"summary.MuFicokm" return the parameter estimations for each level and the result of the Leave-One-Out Cross-Validation (RMSE=Root Mean Squared Error ; Std RMSE=Standardized RMSE ; Q2=explained variance).

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)
	Df <- ExtractNestDesign(DNest,2)
	zf <- Funcf(Df)
#--- Multi-fidelity cokriging creation without parameter estimations
		mymodel <- MuFicokm(
				formula = list(~1,~1), 
				MuFidesign = DNest, 
				response = list(zc,zf), 
				nlevel = 2)

		sum <- summary(object = mymodel, CrossValidation = TRUE)
		names(sum)
#--- Saving parameters
	#--covariance parameters
		sum$Cov.Val
	#--variance parameters
		sum$Var.Val
	#--trend parameters
		sum$Trend.Val
	#-- adjustment parameters
		sum$Rho.Val