summary.gekm: Summary Method for a gekm Object

In gek: Gradient-Enhanced Kriging

Summary Method for a gekm Object

Description

Summarizing (Gradient-Enhanced) Kriging Models.

Usage

## S3 method for class 'gekm'
summary(object, scale = FALSE, ...)

## S3 method for class 'summary.gekm'
print(x, digits = 4L, ...)

Arguments

object	an object of class "gekm".
x	an object of class "summary.gekm".
scale	logical. Should the estimated process standard deviation be scaled? Default is FALSE, see sigma.gekm for details.
digits	number of digits to be used for the print method.
...	further arguments passed to printCoefmat in the print method.

Value

The summary method for an object of class "gekm" returns a list with the following components:

call	the matched call of object.
terms	the terms object used.
coefficients	a matrix with the estimated regression coefficients.
sigma	the estimated (scaled) process standard deviation.
df	degrees of freedom, i.e. the number of observations used to fit the model minus the number of regression coefficients.
cov.scaled	the (scaled) covariance matrix of the estimated regression coefficients.
covtype	the name of the correlation function.
theta	the (estimated) correlation parameteres.

Author(s)

Carmen van Meegen

References

Morris, M., Mitchell, T., and Ylvisaker, D. (1993). Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction. Technometrics, 35(3):243–255. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00401706.1993.10485320")}.

Oakley, J. and O'Hagan, A. (2002). Bayesian Inference for the Uncertainty Distribution of Computer Model Outputs. Biometrika, 89(4):769–784. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/89.4.769")}.

Park, J.-S. and Beak, J. (2001). Efficient Computation of Maximum Likelihood Estimators in a Spatial Linear Model with Power Exponential Covariogram. Computers & Geosciences, 27(1):1–7. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0098-3004(00)00016-9")}.

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. The MIT Press. https://gaussianprocess.org/gpml/.

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

Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989). Design and Analysis of Computer Experiments. Statistical Science, 4(4):409–423. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/ss/1177012413")}.

Santner, T. J., Williams, B. J., and Notz, W. I. (2018). The Design and Analysis of Computer Experiments. 2nd edition. Springer-Verlag.

Stein, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer Series in Statistics. Springer-Verlag. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-1-4612-1494-6")}.

Zimmermann, R. (2015). On the Condition Number Anomaly of Gaussian Correlation Matrices. Linear Algebra and its Applications, 466:512-–526. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.laa.2014.10.038")}.

See Also

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

coef for extracting the (matrix of) coefficients.

vcov for calculating the covaraince matrix of the regression coefficients.

confint for computing confidence intervals for the regression coefficients.

Examples

## 1-dimensional example: Oakley and O’Hagan (2002)

# Define test function and its gradient
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 (gradient-enhanced) Kriging model
km.1d <- gekm(y ~ . + I(x^2), data = dat, covtype = "gaussian", theta = 1)
gekm.1d <- gekm(y ~ . + I(x^2), data = dat, deriv = deri, covtype = "gaussian", theta = 1)

# Model summaries
summary(km.1d)
summary(gekm.1d)
summary(gekm.1d, scale = TRUE)

gek documentation built on Jan. 31, 2026, 1:07 a.m.