covIso-class {DiceKriging}

Class of tensor-product spatial covariances with isotropic range

Description

S4 class of isotropic spatial covariance kerlnes based upon the covTensorProduct class

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)

Slots

d:

Object of class "integer". The spatial dimension.

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.

range.names:

Object of class "character". Names of range parameters, for printing purpose. Default is "theta".

range.val:

Object of class "numeric". Values of range parameters.

Extends

Class "covKernel", directly.

Methods

coef

signature(object = "covIso"): ...

covMat1Mat2

signature(object = "covIso"): ...

covMatrix

signature(object = "covIso"): ...

covMatrixDerivative

signature(object = "covIso"): ...

covParametersBounds

signature(object = "covIso"): ...

covparam2vect

signature(object = "covIso"): ...

vect2covparam

signature(object = "covIso"): ...

covVector.dx

signature(object = "covIso"): ...

inputnames

signature(x = "covIso"): ...

kernelname

signature(x = "covIso"): ...

ninput

signature(x = "covIso"): ...

nuggetflag

signature(x = "covIso"): ...

nuggetvalue

signature(x = "covIso"): ...

show

signature(object = "covIso"): ...

summary

signature(object = "covIso"): ...

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("covIso")