View source: R/integration_design.R
integration_design | R Documentation |
Generic function to build integration points for some sampling criterion.
Available important sampling schemes are "sur"
, "jn"
, "timse"
, "vorob"
and "imse"
.
Each of them corresponds to a sampling criterion.
integration_design(integcontrol = NULL, d = NULL, lower, upper, model = NULL, T = NULL,min.prob=0.001)
integcontrol |
Optional list specifying the procedure to build the integration points and weights, relevant only for the sampling criteria based on numerical integration:
( |
d |
The dimension of the input set. If not provided d is set equal to the length of |
lower |
Vector containing the lower bounds of the design space. |
upper |
Vector containing the upper bounds of the design space. |
model |
A Kriging model of |
T |
Array containing one or several thresholds. |
min.prob |
This argument applies only when importance sampling distributions are chosen. For numerical reasons we give a minimum probability for a point to belong to the importance sample. This avoids potential importance sampling weights equal to infinity. In an importance sample of M points, the maximum weight becomes |
The important sampling aims at improving the accuracy of the computation of criteria which involve numerical integration, like "timse"
, "sur"
, etc.
A list with components:
integration.points |
p * d matrix of p points used for the numerical calculation of integrals |
integration.weights |
Vector of size p corresponding to the weights of each points. If all the points are equally weighted, |
alpha |
If the |
Clement Chevalier (University of Neuchatel, Switzerland)
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. (2013) Fast uncertainty reduction strategies relying on Gaussian process models Ph.D Thesis, University of Bern
max_timse_parallel
, max_sur_parallel
#integration_design #when nothing is specified: integration points #are chosen with the sobol sequence integ.param <- integration_design(lower=c(0,0),upper=c(1,1)) plot(integ.param$integration.points) #an example with pure random integration points integcontrol <- list(distrib="MC",n.points=50) integ.param <- integration_design(integcontrol=integcontrol, lower=c(0,0),upper=c(1,1)) plot(integ.param$integration.points) #an example with important sampling distributions #these distributions are used to compute integral criterion like #"sur","timse" or "imse" #for these, we need a kriging model set.seed(9) N <- 16;testfun <- branin lower <- c(0,0);upper <- c(1,1) design <- data.frame( matrix(runif(2*N),ncol=2) ) response <- testfun(design) model <- km(formula=~., design = design, response = response,covtype="matern3_2") integcontrol <- list(distrib="sur",n.points=200,n.candidates=5000, init.distrib="MC") T <- c(60,100) #we are interested in the set of points where the response is in [60,100] integ.param <- integration_design(integcontrol=integcontrol, lower=c(0,0),upper=c(1,1), model=model,T=T) print_uncertainty_2d(model=model,T=T,type="sur", col.points.init="red",cex.points=2, main="sur uncertainty and one sample of integration points") points(integ.param$integration.points,pch=17,cex=1)
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