yhat: Prediction Function with Modified Kernel

Description

Standard kriging prediction function for the modified correlation functions.

Usage

yhat(newdata, x, y, parameter, covtype = "gauss", eps.R = 1e-08, 
    Cl, iso = FALSE, se.compute=FALSE)

Arguments

newdata

matrix containing the points where to perform predictions

matrix of input data

vector of output data

parameter

(by MLoptimConstrained estimated) kriging parameters, list of size of 'Cl' containing for each clique a list of parameters alpha (single value) and theta (numeric vector of values)

covtype

an optional character string specifying the covariance structure to be used, to be chosen between "gauss", "matern5_2", "matern3_2", "exp" or "powexp" (see DiceKriging), defaults to "gauss"

eps.R

small positive number indicating the nugget effect added to the covariance matrix diagonalk, defaults to eps.R = 1e-08

list of cliques

iso

boolean vector indicating for each clique if it is isotropic (TRUE) or anisotropic (FALSE), defaults to iso = FALSE (all cliques anisotropic)

se.compute

optional boolean. If FALSE, only the kriging mean is computed. If TRUE, the kriging variance (actually, the corresponding standard deviation) is computed, too

Value

meankriging mean computed at newdata.
sdkriging standard deviation computed at newdata. Only computed if se.compute=TRUE.

References

Muehlenstaedt, T.; Roustant, O.; Carraro, L.; Kuhnt, S. (2011) Data-driven Kriging models based on FANOVA-decomposition, Statistics and Computing.

Examples

Run this code

### example for ishigami function with cliques {1,3} and {2}
d <- 3
x <- matrix(runif(100*d,-pi,pi),nc=d)
y <- ishigami.fun(x)

Cl <- list(c(2), c(1,3))

# constrained ML optimation with kernel defined by the cliques
parameter <- MLoptimConstrained(x, y, Cl = Cl)

# prediction with the new model
xpred <- matrix(runif(500 * d,-pi,pi), ncol = d)
ypred <- yhat(xpred, x, y, parameter, Cl=Cl)
yexact <- ishigami.fun(xpred)

# rmse
sqrt(mean((ypred[,1]- yexact)^2))

# scatterplot
par(mfrow=c(1,1))
plot(yexact, ypred[,1], asp = 1)
abline(0, 1)

### compare to one single clique {1,2,3}
Cl <- list(c(1,2,3))

# constrained ML optimation with kernel defined by the cliques
parameter <- MLoptimConstrained(x, y, Cl = Cl)

# prediction with the new model
ypred <- yhat(xpred, x, y, parameter, Cl=Cl)

# rmse
sqrt(mean((ypred$mean- yexact)^2))

# scatterplot
par(mfrow=c(1,1))
plot(yexact, ypred$mean, asp = 1)
abline(0, 1)

### isotropic cliques

Cl <- list(c(2),c(1,3))
parameter <- MLoptimConstrained(x, y, Cl = Cl, iso=c(FALSE,TRUE))
ypred <- yhat(xpred, x, y, parameter, Cl=Cl, iso=c(FALSE,TRUE))
sqrt(mean((ypred$mean- yexact)^2))

# the same since first clique has length 1
parameter <- MLoptimConstrained(x, y, Cl = Cl, iso=c(TRUE,TRUE))
ypred <- yhat(xpred, x, y, parameter, Cl=Cl, iso=c(TRUE,TRUE))
sqrt(mean((ypred$mean- yexact)^2))