plot.gp: Diagnostic Plot for the Validation of a 'gp' Object

In kergp: Gaussian Process Laboratory

Diagnostic Plot for the Validation of a gp Object

Description

Three plots are currently available, based on the influence results: one plot of fitted values against response values, one plot of standardized residuals, and one qqplot of standardized residuals.

Usage

## S3 method for class 'gp'
plot(x, y, kriging.type = "UK",
    trend.reestim = TRUE, which = 1:3, ...)

Arguments

x	An object with S3 class "gp".
y	Not used.
kriging.type	Optional character string corresponding to the GP "kriging" family, to be chosen between simple kriging ("SK") or universal kriging ("UK").
trend.reestim	Should the trend be re-estimated when removing an observation? Default to TRUE.
which	A subset of \{1, 2, 3\} indicating which figures to plot (see Description above). Default is 1:3 (all figures).
...	No other argument for this method.

Details

The standardized residuals are defined by [y(\mathbf{x}_i) - \widehat{y}_{-i}(\mathbf{x}_i)] / \widehat{\sigma}_{-i}(\mathbf{x}_i), where y(\mathbf{x}_i) is the response at the location \mathbf{x}_i, \widehat{y}_{-i}(\mathbf{x}_i) is the fitted value when the i-th observation is omitted (see influence.gp), and \widehat{\sigma}_{-i}(\mathbf{x}_i) is the corresponding kriging standard deviation.

Value

A list composed of the following elements where n is the total number of observations.

mean	A vector of length n. The i-th element is the kriging mean (including the trend) at the i-th observation number when removing it from the learning set.
sd	A vector of length n. The i-th element is the kriging standard deviation at the i-th observation number when removing it from the learning set.

Warning

Only trend parameters are re-estimated when removing one observation. When the number n of observations is small, re-estimated values can substantially differ from those obtained with the whole learning set.

References

F. Bachoc (2013), "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification". Computational Statistics and Data Analysis, 66, 55-69.

N.A.C. Cressie (1993), Statistics for spatial data. Wiley series in probability and mathematical statistics.

O. Dubrule (1983), "Cross validation of Kriging in a unique neighborhood". Mathematical Geology, 15, 687-699.

J.D. Martin and T.W. Simpson (2005), "Use of kriging models to approximate deterministic computer models". AIAA Journal, 43 no. 4, 853-863.

M. Schonlau (1997), Computer experiments and global optimization. Ph.D. thesis, University of Waterloo.

See Also

predict.gp and influence.gp, the predict and influence methods for "gp".

kergp documentation built on April 4, 2025, 2:29 a.m.