Description Usage Arguments Value Author(s) References Examples
Compute Vorob'ev threshold, expectation and deviation. Also, displaying the symmetric deviation function is possible. The symmetric deviation function is the probability for a given target in the objective space to belong to the symmetric difference between the Vorob'ev expectation and a realization of the (random) attained set.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
x 
Either a matrix of data values, or a data frame, or a list of data frames of exactly three columns. The third column gives the set (run, sample, ...) identifier. 
reference 
( 
VE, threshold 
Vorob'ev expectation and threshold, e.g., as returned
by 
nlevels 
number of levels in which is divided the range of the symmetric deviation. 
ve.col 
plotting parameters for the Vorob'ev expectation. 
xlim, ylim, main 
Graphical parameters, see

legend.pos 
the position of the legend, see

col.fun 
function that creates a vector of 
vorobT
returns a list with elements threshold
,
VE
, and avg_hyp
(average hypervolume)
vorobDev
returns the Vorob'ev deviation.
Mickael Binois
BinGinRou2015gaupareaf
C. Chevalier (2013), Fast uncertainty reduction strategies relying on Gaussian process models, University of Bern, PhD thesis.
I. Molchanov (2005), Theory of random sets, Springer.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  data(CPFs)
res < vorobT(CPFs, reference = c(2, 200))
print(res$threshold)
## Display Vorob'ev expectation and attainment function
# First style
eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 25, 50, 75, 100, res$threshold),
main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"),
list(a = formatC(res$threshold, digits = 2, format = "f"))))
# Second style
eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 20, 40, 60, 80, 100),
col = gray(seq(0.8, 0.1, length.out = 6)^0.5), type = "area",
legend.pos = "bottomleft", extra.points = res$VE, extra.col = "cyan",
extra.legend = "VE", extra.lty = "solid", extra.pch = NA, extra.lwd = 2,
main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"),
list(a = formatC(res$threshold, digits = 2, format = "f"))))
# Now print Vorob'ev deviation
VD < vorobDev(CPFs, res$VE, reference = c(2, 200))
print(VD)
# Now display the symmetric deviation function.
symDifPlot(CPFs, res$VE, res$threshold, nlevels = 11)
# Levels are adjusted automatically if too large.
symDifPlot(CPFs, res$VE, res$threshold, nlevels = 200, legend.pos = "none")
# Use a different palette.
symDifPlot(CPFs, res$VE, res$threshold, nlevels = 11, col.fun = heat.colors)

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