R: Diagnostic Plot for the Validation of a 'gp' Object

plot.gp {kergp}

R Documentation

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.

Diagnostic Plot for the Validation of a gp Object