R: Covariance and Variogram Models in 'RandomFields' (RM...

RMmodel {RandomFields} | R Documentation

## Covariance and Variogram Models in RandomFields (RM commands)

### Description

Summary of implemented covariance and variogram models

### Details

To generate a covariance or variogram model for use within RandomFields, calls of the form

RM_name_(..., var, scale, Aniso, proj)

can be used, where _name_ has to be replaced by a valid model name,

- `...` can take model specific arguments.

- `var` is the optional variance argument v,

- `scale` the optional scale argument s,

- `Aniso` an optional anisotropy matrix A or given by `RMangle`, and

- `proj` is the optional projection vector which defines a diagonal matrix of zeros and ones and `proj` gives the positions of the ones (integer values). In a space-time framework, also `"space"` and `"time"` are valid values.

With φ denoting the original model, the transformed model is C(h) = v * φ(A*h/s).

`RM_name_` must be a function of class `RMmodelgenerator`. The return value of all functions `RM_name_` is of class `RMmodel`.

The following models are available (cf. `RFgetModelNames`).

Basic stationary and isotropic models

`RMcauchy` | Cauchy family
`RMexp` | exponential model
`RMgencauchy` | generalized Cauchy family
`RMgauss` | Gaussian model
`RMgneiting` | differentiable model with compact support
`RMmatern` | Whittle-Matern model
`RMnugget` | nugget effect model
`RMspheric` | spherical model
`RMstable` | symmetric stable family or powered exponential model
`RMwhittle` | Whittle-Matern model, alternative parametrization

Variogram models (stationary increments/intrinsically stationary)

`RMfbm` | fractal Brownian motion

Basic Operations

`RMmult`, `*` | product of covariance models
`RMplus`, `+` | sum of covariance models or variograms

Basic models for mixed effect modelling

`RMfixcov` | constant pre-defined covariance
`RMfixed` | fixed or trend effects; Caution: RMfixed is not a function and can be used only in formula notation

Others

`RMtrend` | trend
`RMangle` | defines a 2x2 anisotropy matrix by rotation and stretch arguments.

### Author(s)

Alexander Malinowski, malinowski@math.uni-mannheim.de

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### References

- Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.

- Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.

- Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., Space-Time Processes and Challenges Related to Environmental Problems. New York: Springer.

- Yaglom, A.M. (1987) Correlation Theory of Stationary and Related Random Functions I, Basic Results. New York: Springer.

- Wackernagel, H. (2003) Multivariate Geostatistics. Berlin: Springer, 3nd edition.

### See Also

RM for an overview over more advanced classes of models
RC, RF, RP, RR, R., `RFcov`, `RFformula`, `RMmodelsAdvanced`, `RMmodelsAuxiliary`, trend modelling

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    ## an example of a simple model
    model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget
    plot(model)

[Package RandomFields version 3.1.50 Index]