print_uncertainty_nd: Print a measure of uncertainty for functions with dimension d strictly higher than 2.

Description

This function draws projections on various plans of a given measure of uncertainty. Possible measures are "pn" (probability of excursion) and measures specific to a sampling criterion: "sur", "timse" and "imse". This function can be used to print relevant outputs after having used the function EGI.

Usage

print_uncertainty_nd(model,T,type="pn",lower=NULL,upper=NULL,
  		resolution=20, nintegpoints=400,main="",
			cex.main=1,cex.lab=1,cex.contourlab=1,cex.axis=1,
			nlevels=10,levels=NULL,
			xdecal=3,ydecal=3, option="mean")

Arguments

model

Kriging model of km class.

Target value (a real number). The sampling algorithm and the underlying kriging model aim to find the points below (resp. over) T.

type

Type of uncertainty that the user wants to print. Possible values are "pn" (probability of excursion), or "sur", "imse", "timse" if we print a measure of uncertainty corresponding to one criterion.

lower

Vector containing the lower bounds of the input domain. If nothing is set we use a vector of 0.

upper

Vector containing the upper bounds of the input domain. If nothing is set we use a vector of 1.

resolution

Number of points to discretize a plan included in the domain. For the moment, we cannot use values higher than 40.

nintegpoints

to do

main

Title of the graph.

cex.main

Multiplicative factor for the size of the title.

cex.lab

Multiplicative factor for the size of titles of the axis.

cex.contourlab

Multiplicative factor for the size of labels of the contour plot.

cex.axis

Multiplicative factor for the size of the axis graduations.

nlevels

Integer corresponding to the number of levels of the contour plot.

levels

Array: one can directly set the levels of the contour plot.

xdecal

Optional position shifting of the titles of the x axis.

ydecal

Optional position shifting of the titles of the y axis.

option

Optional argument (a string). The 3 possible values are "mean" (default), "max" and "min".

Value

the integrated uncertainty

References

Bect J., Ginsbourger D., Li L., Picheny V., Vazquez E. (2010), Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, pp.1-21, 2011, http://arxiv.org/abs/1009.5177

Examples

Run this code

# NOT RUN {
#print_uncertainty_nd

set.seed(8)
N <- 25 #number of observations
T <- -1 #threshold
testfun <- hartman3
#The hartman3 function is defined over the domain [0,1]^3. 

hartman3(runif(3))

lower <- rep(0,times=3)
upper <- rep(1,times=3)

#a 9 points initial design (LHS in 3 dimensions)
design <- data.frame( matrix(runif(3*N),ncol=3) )
response <- apply(design,1,testfun)

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

# }
# NOT RUN {
print_uncertainty_nd(model=model,T=T,main="average probability of excursion",type="pn",
                    option="mean")

print_uncertainty_nd(model=model,T=T,main="maximum probability of excursion",type="pn",
                     option="max")

# }