predict_nobias_km {KrigInv}

Kriging predictions

Description

This function is similar to the predict.km function from the DiceKriging package. The only change is the additionnal F.newdata output.

Usage

predict_nobias_km(object, newdata, type = "UK", 
se.compute = TRUE, cov.compute = FALSE, low.memory=FALSE,...)

Arguments

object

A Kriging model of km class.

newdata

Vector, matrix or data frame containing the points where to perform predictions.

type

Character string corresponding to the kriging family, to be chosen between simple kriging ("SK"), or universal kriging ("UK").

se.compute

Optional boolean. If FALSE, only the kriging mean is computed. If TRUE, the kriging standard deviation and confidence intervals are computed too.

cov.compute

Optional boolean. If TRUE the conditional covariance matrix is computed.

low.memory

Optional boolean. If set to TRUE the function will only return kriging means and standard deviations.

...

No other arguments.

Value

mean

kriging mean (including the trend) computed at newdata.

sd

kriging standard deviation computed at newdata. Not computed if se.compute=FALSE.

cov

kriging conditional covariance matrix. Not computed if cov.compute=FALSE (default).

lower95

upper95

bounds of the 95 % confidence interval computed at newdata (to be interpreted with special care when parameters are estimated, see description above). Not computed if se.compute=FALSE.

c

an auxiliary matrix, containing all the covariances between newdata and the initial design points.

Tinv.c

an auxiliary vector, equal to T^(-1)*c.

F.newdata

value of the trend function at newdata.

Warning

Beware that the only consistency check between newdata and the experimental design is to test whether they have same number of columns. In that case, the columns of newdata are interpreted in the same order as the initial design.

Author(s)

O. Roustant (Ecole des Mines de St-Etienne, France)

David Ginsbourger (IDIAP Martigny and University of Bern, Switzerland)

References

N.A.C. Cressie (1993), Statistics for spatial data, Wiley series in probability and mathematical statistics.

A.G. Journel and C.J. Huijbregts (1978), Mining Geostatistics, Academic Press, London.

D.G. Krige (1951), A statistical approach to some basic mine valuation problems on the witwatersrand, J. of the Chem., Metal. and Mining Soc. of South Africa, 52 no. 6, 119-139.

J.D. Martin and T.W. Simpson (2005), Use of kriging models to approximate deterministic computer models, AIAA Journal, 43 no. 4, 853-863.

G. Matheron (1963), Principles of geostatistics, Economic Geology, 58, 1246-1266.

G. Matheron (1969), Le krigeage universel, Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau, 1.

J.-S. Park and J. Baek (2001), Efficient computation of maximum likelihood estimators in a spatial linear model with power exponential covariogram, Computer Geosciences, 27 no. 1, 1-7.

C.E. Rasmussen and C.K.I. Williams (2006), Gaussian Processes for Machine Learning, the MIT Press, https://gaussianprocess.org/gpml/

J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn (1989), Design and analysis of computer experiments, Statistical Science, 4, 409-435.

See Also

predict.km, km

Examples

#predict_nobias_km
set.seed(9)
N <- 20 #number of observations
testfun <- branin

#a 20 points initial design
design <- data.frame( matrix(runif(2*N),ncol=2) )
response <- testfun(design)

#km object with matern3_2 covariance
#params estimated by ML from the observations
model <- km(formula=~., design = design, 
	response = response,covtype="matern3_2")

n.grid <- 100
x.grid <- y.grid <- seq(0,1,length=n.grid)

newdata <- expand.grid(x.grid,y.grid)
pred <- predict_nobias_km(object=model,newdata=newdata,type="UK",se.compute=TRUE)

z.grid1 <- matrix(pred$mean, n.grid, n.grid)
z.grid2 <- matrix(pred$sd, n.grid, n.grid)

par(mfrow=c(1,2))

#plots: contour of the kriging mean and stdev
image(x=x.grid,y=y.grid,z=z.grid1,col=grey.colors(10))
contour(x=x.grid,y=y.grid,z=z.grid1,15,add=TRUE)
points(design, col="black", pch=17, lwd=4,cex=2)
title("Kriging mean")

image(x=x.grid,y=y.grid,z=z.grid2,col=grey.colors(10))
contour(x=x.grid,y=y.grid,z=z.grid2,15,add=TRUE)
points(design, col="black", pch=17, lwd=4,cex=2)
title("Kriging standard deviation")