pGPx (version 0.1.4)

simulate_and_interpolate: Simulate and interpolate

Description

Generates nsims approximate posterior field realizations at interpolatepoints. The approximate realizations are computed by simulating the field only at simupoints simulation points.

Usage

simulate_and_interpolate(
  object,
  nsim = 1,
  simupoints = NULL,
  interpolatepoints = NULL,
  nugget.sim = 0,
  type = "UK"
)

Value

A matrix nsim*interpolatepoints containing the approximate realizations.

Arguments

object

km object

nsim

numbero of simulations

simupoints

simulations points, locations where the field was simulated

interpolatepoints

points where posterior simulations are approximated

nugget.sim

nugget to be added to simulations for numerical stability

type

type of kriging model used for approximation (default Universal Kriging)

References

Azzimonti D. F., Bect J., Chevalier C. and Ginsbourger D. (2016). Quantifying uncertainties on excursion sets under a Gaussian random field prior. SIAM/ASA Journal on Uncertainty Quantification, 4(1):850–874.

Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern.

Examples

### Simulate and interpolate for a 2d example
if (!requireNamespace("DiceKriging", quietly = TRUE)) {
stop("DiceKriging needed for this example to work. Please install it.",
     call. = FALSE)
}
if (!requireNamespace("DiceDesign", quietly = TRUE)) {
stop("DiceDesign needed for this example to work. Please install it.",
     call. = FALSE)
}
# Define the function
g=function(x){
  return(-DiceKriging::branin(x))
}
d=2
# Fit OK km model
design<-DiceDesign::maximinESE_LHS(design = DiceDesign::lhsDesign(n=50,
                                                                  dimension = 2,
                                                                  seed=42)$design)$design
colnames(design)<-c("x1","x2")
observations<-apply(X = design,MARGIN = 1,FUN = g)
kmModel<-DiceKriging::km(formula = ~1,design = design,response = observations,
                         covtype = "matern3_2",control=list(trace=FALSE))
# Get simulation points
# Here they are not optimized, you can use optim_dist_measure to find optimized points
simu_points <- DiceDesign::maximinSA_LHS(DiceDesign::lhsDesign(n=100,
                                                               dimension = d,
                                                               seed=1)$design)$design
# obtain nsims posterior realization at simu_points
nsims <- 1
nn_data<-expand.grid(seq(0,1,,50),seq(0,1,,50))
nn_data<-data.frame(nn_data)
colnames(nn_data)<-colnames(kmModel@X)
approx.simu <- simulate_and_interpolate(object=kmModel, nsim = 1, simupoints = simu_points,
                                        interpolatepoints = as.matrix(nn_data),
                                        nugget.sim = 0, type = "UK")
# \donttest{
## Plot the approximate process realization
image(matrix(approx.simu[1,],ncol=50),
      col=grey.colors(20))
contour(matrix(approx.simu[1,],ncol=50),
        nlevels = 20,add=TRUE)

# }