Kriging: Create an object with S3 class '"Kriging"' using the...

In rlibkriging: Kriging Models using the 'libKriging' Library

Create an object with S3 class "Kriging" using the libKriging library.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

Kriging(
  y = NULL,
  X = NULL,
  kernel = NULL,
  regmodel = c("constant", "linear", "interactive"),
  normalize = FALSE,
  optim = c("BFGS", "Newton", "none"),
  objective = c("LL", "LOO", "LMP"),
  parameters = NULL
)

Arguments

y	Numeric vector of response values.
X	Numeric matrix of input design.
kernel	Character defining the covariance model: "exp", "gauss", "matern3_2", "matern5_2".
regmodel	Universal Kriging linear trend.
normalize	Logical. If TRUE both the input matrix X and the response y in normalized to take values in the interval [0, 1].
optim	Character giving the Optimization method used to fit hyper-parameters. Possible values are: "BFGS", "Newton" and "none", the later simply keeping the values given in parameters. The method "BFGS" uses the gradient of the objective. The method "Newton" uses both the gradient and the Hessian of the objective.
objective	Character giving the objective function to optimize. Possible values are: "LL" for the Log-Likelihood, "LOO" for the Leave-One-Out sum of squares and "LMP" for the Log-Marginal Posterior.
parameters	Initial values for the hyper-parameters. When provided this must be named list with elements "sigma2" and "theta" containing the initial value(s) for the variance and for the range parameters. If theta is a matrix with more than one row, each row is used as a starting point for optimization.

Value

An object with S3 class "Kriging". Should be used with its predict, simulate, update methods.

Author(s)

Yann Richet [e-mail]

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
## fit and print
k <- Kriging(y, X, kernel = "matern3_2")
print(k)

x <- as.matrix(seq(from = 0, to = 1, length.out = 101))
p <- predict(k, x = x, stdev = TRUE, cov = FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
border = NA, col = rgb(0, 0, 1, 0.2))

s <- simulate(k, nsim = 10, seed = 123, x = x)

matlines(x, s, col = rgb(0, 0, 1, 0.2), type = "l", lty = 1)

rlibkriging documentation built on July 9, 2023, 5:53 p.m.