rlibkriging (version 0.9-1)

Kriging: 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", "none"),
  normalize = FALSE,
  optim = c("BFGS", "Newton", "none"),
  objective = c("LL", "LOO", "LMP"),
  parameters = NULL
)

Value

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

methods.

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: "constant", "linear", "interactive", "quadratic".

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 (note that "BGFS10" means 10 multi-start of BFGS). 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.

Author

Yann Richet

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, return_stdev = TRUE, return_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)