# Simulates Conditional Process Paths Simulates process paths conditional on a fitted `gekm` model. UTF-8 ```r ## 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. ## Returns - **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. ## References Cressie, N. A. C. (1993). **Statistics for Spartial Data**. John Wiley & Sons. tools:::Rd_expr_doi("10.1002/9781119115151") . Ripley, B. D. (1981). **Spatial Statistics**. John Wiley & Sons. tools:::Rd_expr_doi("10.1002/0471725218") . ## Author(s) Carmen van Meegen ## 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 ```r ## 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)") ```

simulate.gekm function