computeAuxVariables {DiceKriging}R Documentation

Auxiliary variables for kriging

Description

Computes or updates some auxiliary variables used for kriging (see below). This is useful in several situations : when all parameters are known (as for one basic step in Bayesian analysis), or when some new data is added but one does not want to re-estimate the model coefficients. On the other hand, computeAuxVariables is not used during the estimation of covariance parameters, since this function requires to compute the trend coefficients at each optimization step; the alternative given by (Park, Baek, 2001) is preferred.

Usage

computeAuxVariables(model)

Arguments

model an object of class km with missing (or non updated) items.

Value

An updated km objet, where the changes concern the following items:

C0 a matrix representing the covariance matrix for the locations specified in model, when there is no nugget effect nor observation noise.
C a matrix equal to the covariance matrix (including a possible nugget or observation noise).
T a matrix equal to the upper triangular factor of the Choleski decomposition of C, such that t(T)*T = C.
z a vector equal to inv(t(T))*(y - F*beta), with y, F, beta are respectively the response, the experimental matrix and the trend coefficients specified in model.
M a matrix equal to inv(t(T))*F.

Note

C0 and C are computed with covMatrix. T is computed with the base function chol. z and M are computed by solving triangular linear systems with backsolve.

Author(s)

O. Roustant, D. Ginsbourger, Ecole des Mines de St-Etienne

References

J.-S. Park and J. Baek (2001), Efficient computation of maximum likelihood estimators in a spatial linear model with power exponential covariogram, Computer Geosciences, 27 no. 1, 1-7.

See Also

covMatrix, chol, backsolve.


[Package DiceKriging version 1.0 Index]