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

 ```1 2``` ```## S3 method for class 'MuFicokm' 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.

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`).

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 δ_i(x) with δ_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 δ_i(x) with δ_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 δ_i(x) with δ_1(x) = Z_1(x). (see `"MuFicokm"`) `Rho.val ` a list of vectors giving the values of the trends γ_i of the adjustment parameters ρ_i of the cokriging model. The element i of the list corresponds to the adjustment parameter between Z_i and δ_i(x). (see `"MuFicokm"`) `Trend.val ` a list of vectors giving the values of the trend parameters of the Gaussian processes δ_i(x) and Z_1(x).

Loic Le Gratiet

Examples

 ``` 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 26 27 28``` ```#--- 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 ```

MuFiCokriging documentation built on May 30, 2017, 7:01 a.m.