simulate.gekm: Simulates Conditional Process Paths

In gek: Gradient-Enhanced Kriging

Simulates Conditional Process Paths

Description

Simulates process paths conditional on a fitted gekm model.

Usage

## S3 method for class 'gekm'
simulate(object, nsim = 1, seed = NULL, newdata = NULL, tol = NULL, ...)

Arguments

object	an object of class "gekm".
nsim	number of simulated process paths. Default is 1.
seed	argument is not supported.
newdata	a data.frame containing the points where the process in object should be evaluated.
tol	a tolerance for the conditional number of the conditional correlation matrix of newdata, see blockChol for details. Default is NULL, i.e. no regularization is applied.
...	further arguments, not used.

Value

val	a matrix with nrow(newdata) rows and nsim columns of simulated response values at the points of newdata. Each column represents one conditional simulated process path.

Author(s)

Carmen van Meegen

References

Cressie, N. A. C. (1993). Statistics for Spartial Data. John Wiley & Sons. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/9781119115151")}.

Ripley, B. D. (1981). Spatial Statistics. John Wiley & Sons. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/0471725218")}.

See Also

gekm for fitting a (gradient-enhanced) Kriging model.

predict.gekm for prediction at new data points based on a model of class "gekm".

Examples

## 1-dimensional example

# Define test function and its gradient from Oakley and O’Hagan (2002)
f <- function(x) 5 + x + cos(x)
fGrad <- function(x) 1 - sin(x)

# Generate coordinates and calculate slopes
x <- seq(-5, 5, length = 5)
y <- f(x)
dy <- fGrad(x)
dat <- data.frame(x, y)
deri <- data.frame(x = dy)

# Fit Kriging model
km.1d <- gekm(y ~ x, data = dat, covtype = "gaussian", theta = 1)

# Fit Gradient-Enhanced Kriging model
gekm.1d <- gekm(y ~ x, data = dat, deriv = deri, covtype = "gaussian", theta = 1)

# Generate new data for prediction and simulation
newdat <- data.frame(x = seq(-6, 6, length = 600))

# Prediction for both models
pred.km.1d <- predict(km.1d, newdat)
pred.gekm.1d  <- predict(gekm.1d, newdat)

# Simulate process path conditional on fitted models
set.seed(1)
n <- 50
sim.km.1d <- simulate(km.1d, nsim = n, newdata = newdat, tol = 35)
sim.gekm.1d <- simulate(gekm.1d, nsim = n, newdata = newdat, tol = 35)

par(mfrow = c(1, 2), oma = c(3.5, 3.5, 0, 0.2), mar = c(0, 0, 1.5, 0))
matplot(newdat$x, sim.km.1d, type = "l", lty = 1, col = 2:8, lwd = 1, 
	ylim = c(-1, 12), main = "Kriging")
lines(newdat$x, pred.km.1d$fit + qnorm(0.975) * pred.km.1d$sd, lwd = 1.5)
lines(newdat$x, pred.km.1d$fit - qnorm(0.975) * pred.km.1d$sd, lwd = 1.5)
points(x, y, pch = 16, cex = 1)

matplot(newdat$x, sim.gekm.1d, type = "l", lty = 1, col = 2:8, 
	lwd = 1, ylim = c(-1, 12), main = "GEK", yaxt = "n")
lines(newdat$x, pred.gekm.1d$fit + qnorm(0.975) * pred.gekm.1d$sd, lwd = 1.5)
lines(newdat$x, pred.gekm.1d$fit - qnorm(0.975) * pred.gekm.1d$sd, lwd = 1.5)
points(x, y, pch = 16, cex = 1)

mtext(side = 1, outer = TRUE, line = 2.5, "x")
mtext(side = 2, outer = TRUE, line = 2.5, "f(x)")

gek documentation built on April 4, 2025, 12:35 a.m.