R: Auxiliary variables for kriging

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:

`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 `model@trend.coef`. If `model@trend.coef` 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 `model@trend.coef` 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`.

[Package DiceKriging version 1.6.0 Index]