R: Class "covAffineScaling"

covAffineScaling-class {DiceKriging} | R Documentation

## Class "covAffineScaling"

### Description

Composition of isotropic kernels with coordinatewise non-linear scaling obtained by integrating affine functions

### Objects from the Class

In 1-dimension, the covariance kernels are parameterized as in (Rasmussen, Williams, 2006). Denote by `theta` the range parameter, `p` the exponent parameter (for power-exponential covariance), `s` the standard deviation, and `h=|x-y|`. Then we have `C(x,y) = s^2 * k(x,y)`, with:

Gauss | `k(x,y) = exp(-1/2*(h/theta)^2)`
Exponential | `k(x,y) = exp(-h/theta)`
Matern(3/2) | `k(x,y) = (1+sqrt(3)*h/theta)*exp(-sqrt(3)*h/theta)`
Matern(5/2) | `k(x,y) = (1+sqrt(5)*h/theta+(1/3)*5*(h/theta)^2)`
| `*exp(-sqrt(5)*h/theta)`
Power-exponential | `k(x,y) = exp(-(h/theta)^p)`

Here, in every dimension, the corresponding one-dimensional stationary kernel `k(x,y)` is replaced by `k(f(x),f(y))`, where `f` is a continuous monotonic function indexed by 2 parameters (see the references for more detail).

### Slots

`d`:

  Object of class `"integer"`. The spatial dimension.

`knots`:

  Object of class `"numeric"`. A vector specifying the position of the two knots, common to all dimensions.

`eta`:

  Object of class `"matrix"`. A d*2 matrix of scaling coefficients, parametrizing the coordinatewise transformations in the d dimensions.

`name`:

  Object of class `"character"`. The covariance function name. To be chosen between `"gauss", "matern5_2", "matern3_2", "exp"`, and `"powexp"`

`paramset.n`:

  Object of class `"integer"`. 1 for covariance depending only on the ranges parameters, 2 for "powexp" which also depends on exponent parameters.

`var.names`:

  Object of class `"character"`. The variable names.

`sd2`:

  Object of class `"numeric"`. The variance of the stationary part of the process.

`known.covparam`:

  Object of class `"character"`. Internal use. One of: "None", "All".

`nugget.flag`:

  Object of class `"logical"`. Is there a nugget effect?

`nugget.estim`:

  Object of class `"logical"`. Is the nugget effect estimated or known?

`nugget`:

  Object of class `"numeric"`. If there is a nugget effect, its value (homogeneous to a variance).

`param.n`:

  Object of class `"integer"`. The total number of parameters.

### Extends

Class `"covKernel"`, directly.

### Methods

coef

  `signature(object = "covAffineScaling")`: ...

covMat1Mat2

  `signature(object = "covAffineScaling")`: ...

covMatrix

  `signature(object = "covAffineScaling")`: ...

covMatrixDerivative

  `signature(object = "covAffineScaling")`: ...

covParametersBounds

  `signature(object = "covAffineScaling")`: ...

covparam2vect

  `signature(object = "covAffineScaling")`: ...

vect2covparam

  `signature(object = "covAffineScaling")`: ...

inputnames

  `signature(x = "covAffineScaling")`: ...

kernelname

  `signature(x = "covAffineScaling")`: ...

ninput

  `signature(x = "covAffineScaling")`: ...

nuggetflag

  `signature(x = "covAffineScaling")`: ...

nuggetvalue

  `signature(x = "covAffineScaling")`: ...

show

  `signature(object = "covAffineScaling")`: ...

summary

  `signature(object = "covAffineScaling")`: ...

### Author(s)

O. Roustant, D. Ginsbourger

### References

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

C.E. Rasmussen and C.K.I. Williams (2006), Gaussian Processes for Machine Learning, the MIT Press, http://www.GaussianProcess.org/gpml

M.L. Stein (1999), Interpolation of spatial data, some theory for kriging, Springer.

### See Also

`km` `covTensorProduct`

### Examples

    showClass("covAffineScaling")

[Package DiceKriging version 1.5.5 Index]