simulate_and_interpolate: Simulate and interpolate

In pGPx: Pseudo-Realizations for Gaussian Process Excursions

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"
)

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)

Value

A matrix nsim*interpolatepoints containing the approximate realizations.

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")

## 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)

pGPx documentation built on Aug. 23, 2023, 5:09 p.m.