computeQuickKrigcov {KrigInv}

Quick computation of kriging covariances

Description

Computes kriging covariances between some new points and many integration points, using precomputed data.

Usage

computeQuickKrigcov(model,integration.points,X.new,
precalc.data, F.newdata , c.newdata)

Arguments

model

A Kriging model of km class.

integration.points

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

X.new

q*d matrix of new points. The calculated covariances are the covariances between these new point and the integration points.

precalc.data

List containing precalculated data. This list is generated using the function precomputeUpdateData.

F.newdata

The value of the kriging trend basis function at point X.new.

c.newdata

The (unconditional) covariance between X.new and the design points.

Details

This function requires to use another function in order to generate the proper arguments. The argument precalc.data can be generated using precomputeUpdateData. The arguments F.newdata and c.newdata can be obtained using predict_nobias_km.

Value

Matrix of size p*q containing kriging covariances

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

Chevalier C., Ginsbourger D. (2014), Corrected Kriging update formulae for batch-sequential data assimilation, in Pardo-Iguzquiza, E., et al. (Eds.) Mathematics of Planet Earth, pp 119-122

See Also

precomputeUpdateData, predict_nobias_km

Examples

#computeQuickKrigcov

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")

#the integration.points are the points where we want to 
#compute predictions/covariances if a point new.x is added 
#to the DOE
x.grid <- seq(0,1,length=20)
integration.points <- expand.grid(x.grid,x.grid)
integration.points <- as.matrix(integration.points)

#precalculation
precalc.data <- precomputeUpdateData(model=model,
                     integration.points=integration.points)

#now we can compute quickly kriging covariances 
#between these data and any other points.
#example if 5 new points are added:
X.new <- matrix(runif(10),ncol=2)
pred <- predict_nobias_km(object=model,
                          newdata=X.new,type="UK",se.compute=TRUE)

kn <- computeQuickKrigcov(model=model,
                    integration.points=integration.points,X.new=X.new,
                    precalc.data=precalc.data,
                    F.newdata=pred$F.newdata,
                    c.newdata=pred$c)