excursion_probability {KrigInv}

Excursion probability with one or many thresholds

Description

Probability that Gaussian random variables with some mean and variance are over a threshold T, or in an union of intervals. If T is a vector of size p, T1,T2,...,Tp then the considered union of interval is (T1,T2) U ... U (Tp, +infty) if p is odd, and (T1,T2) U ... U (Tp-1, Tp) if p is even.

Usage

excursion_probability(mn,sn,T)

Arguments

mn

Array of size k containing the expectations of the Gaussian random variables.

sn

Array of size k containing the standard deviations of the Gaussian random variables.

T

Array containing one or several thresholds.

Value

Array of size k containing the k excursion probabilities.

Author(s)

Clement Chevalier (University of Neuchatel, Switzerland)

References

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2014), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set, Technometrics, vol. 56(4), pp 455-465

See Also

predict_nobias_km

Examples

#excursion_probability

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")

some_points <- matrix(runif(20),ncol=2)
pred <- predict_nobias_km(object = model,newdata = some_points,
                type = "UK",se.compute = TRUE)
                
T <- c(60,80,100)
excursion_probability(mn = pred$mean,sn = pred$sd,T=T)
# probability to be in the interval [60,80] U [100, infty]