computeAuxVariables: Auxiliary variables for kriging

In DiceKriging: Kriging Methods for Computer Experiments

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:

T	a matrix equal to the upper triangular factor of the Choleski decomposition of C, such that t(T)*T = C (where C is the covariance matrix).
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 [e-mail]. If [e-mail] is empty, z is not computed.
M	a matrix equal to inv(t(T))*F.

Note

T is computed with the base function chol. z and M are computed by solving triangular linear systems with backsolve. z is not computed if [e-mail] is empty.

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.

DiceKriging documentation built on Feb. 24, 2021, 1:07 a.m.