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Last data update: 2014.03.03

R: Prediction Function with Modified Kernel

predictAdditive

R Documentation

Prediction Function with Modified Kernel

Description

Standard kriging prediction function for the modified correlation functions.

Usage

predictAdditive(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
`x`	matrix of input data
`y`	vector of output data
`parameter`	(by `kmAdditive` 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`
`cl`	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

`mean`	kriging mean computed at `newdata`.
`sd`	kriging standard deviation computed at `newdata`. Only computed if `se.compute=TRUE`.

Author(s)

T. Muehlenstaedt, O. Roustant, J. Fruth

References

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

Examples

### 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 <- kmAdditive(x, y, cl = cl)

# prediction with the new model
xpred <- matrix(runif(500 * d,-pi,pi), ncol = d)
ypred <- predictAdditive(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 <- kmAdditive(x, y, cl = cl)

# prediction with the new model
ypred <- predictAdditive(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 <- kmAdditive(x, y, cl = cl, iso=c(FALSE,TRUE))
ypred <- predictAdditive(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 <- kmAdditive(x, y, cl = cl, iso=c(TRUE,TRUE))
ypred <- predictAdditive(xpred, x, y, parameter, cl=cl, iso=c(TRUE,TRUE))
sqrt(mean((ypred$mean- yexact)^2))