KrigInv (version 1.3.1)

computeRealVolumeConstant: A constant used to calculate the expected excursion set's volume variance

Description

This function computes a constant used to calculate exactly the value of the "jn" criterion at one point. Computing this constant does NOT change the optimum of the "jn" criterion. Therefore, its calculation is indicative only and is only necessary to know exactly (in expectation) the excursion set's volume variance.

Usage

computeRealVolumeConstant(model,integration.points,
integration.weights=NULL,T)

Arguments

model

A Kriging model of km class.

integration.points

p*d matrix of points for numerical integration in the X space.

integration.weights

(Optional) Vector of size p corresponding to the weights of these integration points. If not provided, all weights are set to 1.

T

the targeted (scalar) output value

Value

a scalar

References

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set ,http://hal.archives-ouvertes.fr/hal-00641108/

Chevalier C., Ginsbourger D. (2012), Corrected Kriging update formulae for batch-sequential data assimilation ,http://arxiv.org/pdf/1203.6452.pdf

See Also

precomputeUpdateData, predict_nobias_km, predict_update_km

Examples

# NOT RUN {
#computeRealVolumeConstant

set.seed(8)
N <- 9 #number of observations
testfun <- branin
T <- 80

#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")

integcontrol <- list(n.points=50,distrib="sur",init.distrib="MC")
obj <- integration_design(integcontrol=integcontrol,
	lower=c(0,0),upper=c(1,1),
model=model,T=T)
integration.points <- obj$integration.points
integration.weights <- obj$integration.weights

# }
# NOT RUN {
computeRealVolumeConstant(model=model,
	integration.points=integration.points,
        integration.weights=integration.weights,T=T)
# }