print_uncertainty_2d: Prints a measure of uncertainty for 2d function.

Description

This function draws the value of a given measure of uncertainty over the whole input domain (2D). 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_2d(model, T, type = "pn", 
lower = c(0, 0), upper = c(1, 1), resolution = 200, 
new.points = 0, xlab = "", ylab = "", main = "", 
xscale = c(0, 1), yscale = c(0, 1), show.points = TRUE, 
cex.main = 1, cex.lab = 1, cex.contourlab = 1, cex.points = 1, 
cex.axis = 1, pch.points.init = 17, pch.points.end = 17, 
col.points.init = "black", col.points.end = "red", nlevels = 10, 
levels = NULL, xaxislab = NULL, yaxislab = NULL, 
xaxispoint = NULL, yaxispoint = NULL, xdecal = 3, ydecal = 3,
krigmeanplot=FALSE,vorobmean=FALSE)

Arguments

model

Kriging model of km class.

Target value (scalar).

type

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

lower

Vector containing the lower bounds of the input domain.

upper

Vector containing the upper bounds of the input domain.

resolution

Number of points to discretize the domain. This discretization is used in each dimension, so that the total number of points is resolution^2.

new.points

Number of new observations. These observations are the last new.points observations and can be printed in another color and the initial observations (see argument: col.points.end).

xlab

Label for the x axis.

ylab

Label for the y axis.

main

Title of the graph.

xscale

If one wants to rescale the input domain on another interval it is possible to set this vector of size 2. The new interval will be translated by xscale[1] and expanded by a factor xscale[2] - xscale[1].

yscale

see: xscale.

show.points

Boolean: should we show the observations on 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.points

Multiplicative factor for the size of the points.

cex.axis

Multiplicative factor for the size of the axis graduations.

pch.points.init

Symbol for the n-new.points first observations.

pch.points.end

Symbol for the new.points last observations.

col.points.init

Color for the n-new.points first observations.

col.points.end

Color for the new.points last observations.

nlevels

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

levels

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

xaxislab

Optional new labels that will replace the normal levels on x axis.

yaxislab

Optional new labels that will replace the normal levels on y axis.

xaxispoint

Position of these new labels on x axis.

yaxispoint

Position of these new labels on y axis.

xdecal

Optional position shifting of the titles of the x axis.

ydecal

Optional position shifting of the titles of the y axis.

krigmeanplot

Optional boolean. When it is set to FALSE (default) the contour plot corresponds to the uncertainty selected. When it is set to TRUE the contour plot gives the kriging mean.

vorobmean

Optional boolean. When it is set to TRUE the Vorob'ev expectation is plotted. It corresponds to the averaged excursion set, using the definition of Vorob'ev.

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_2d

set.seed(8)
N <- 9 #number of observations
T <- 80 #threshold
testfun <- branin
lower <- c(0,0)
upper <- c(1,1)

#a 9 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")

print_uncertainty_2d(model=model,T=T,main="probability of excursion",
                     type="pn",krigmeanplot=TRUE)

#print_uncertainty_2d(model=model,T=T,main="vorob uncertainty",
#type="vorob",krigmeanplot=FALSE)

#print_uncertainty_2d(model=model,T=T,main="imse uncertainty",
#type="imse",krigmeanplot=FALSE)

#print_uncertainty_2d(model=model,T=T,main="timse uncertainty",
#type="timse",krigmeanplot=FALSE)

#print_uncertainty_2d(model=model,T=T,main="sur 
#uncertainty",type="sur",krigmeanplot=FALSE)

#print_uncertainty_2d(model=model,T=T,main="probability of excursion",
#                     type="pn",krigmeanplot=TRUE,vorobmean=TRUE)

# }