vorob_threshold {KrigInv}

Calculation of the Vorob'ev threshold

Description

Evaluation of the Vorob'ev threshold given an excursion probability vector. This threshold is such that the volume of the set (x : pn(x) > threshold) is equal to the integral of pn.

Usage

vorob_threshold(pn)

Arguments

pn

Input vector of arbitrary size containing the excursion probabilities pn(x).

Details

In this function, all the points x are supposed to be equaly weighted.

Value

a scalar: the Vorob'ev thresold

Author(s)

Clement Chevalier (University of Neuchatel, Switzerland)

References

Chevalier C., Ginsbouger D., Bect J., Molchanov I. (2013) Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with gaussian process models mODa 10, Advances in Model-Oriented Design and Analysis, Contributions to Statistics, pp 35-43

Chevalier C. (2013) Fast uncertainty reduction strategies relying on Gaussian process models Ph.D Thesis, University of Bern

See Also

max_vorob_parallel, vorob_optim_parallel

Examples

#vorob_threshold

set.seed(9)
N <- 20 #number of observations
T <- 80 #threshold
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")

## Not run: 
###we need to compute some additional arguments:
#integration points, and current kriging means and variances at these points
integcontrol <- list(n.points=50,distrib="sobol")
obj <- integration_design(integcontrol=integcontrol,
lower=c(0,0),upper=c(1,1),model=model,T=T)

integration.points <- obj$integration.points

pred <- predict_nobias_km(object=model,newdata=integration.points,
type="UK",se.compute=TRUE)
pn <- pnorm((pred$mean-T)/pred$sd)

vorob_threshold(pn)

## End(Not run)