computeRealVolumeConstant {KrigInv}

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. 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

Target threshold.

Details

Note that, even if the "jn" criterion can be used with more than one threshold, the computation of this constant is implemented only when the number of threshold is equal to 1.

Value

a scalar

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

precomputeUpdateData, predict_nobias_km

Examples

#computeRealVolumeConstant

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

#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")

integcontrol <- list(n.points=500,distrib="jn",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)

## End(Not run)