R: Advanced features of the mdoels

RMmodelsAdvanced {RandomFields} | R Documentation

## Advanced features of the mdoels

### Description

Here, further models and advanced comments for `RMmodel` are given. See also `RFgetModelNames`.

### Details

Further stationary and isotropic models

`RMaskey` | Askey model (generalized test or triangle model)
`RMbcw` | bridging model between `RMcauchy` and `RMgenfbm`
`RMbessel` | Bessel family
`RMcircular` | circular model
`RMconstant` | spatially constant model
`RMcubic` | cubic model (see Chiles \& Delfiner)
`RMdagum` | Dagum model
`RMdampedcos` | exponentially damped cosine
`RMqexp` | Variant of the exponential model
`RMfractdiff` | fractionally differenced process
`RMfractgauss` | fractional Gaussian noise
`RMgengneiting` | generalized Gneiting model
`RMgneitingdiff` | Gneiting model for tapering
`RMhyperbolic` | generalised hyperbolic model
`RMlgd` | Gneiting's local-global distinguisher
`RMlsfbm` locally stationary fractal Brownian motion
`RMpenta` | penta model (see Chiles \& Delfiner)
`RMpower` | Golubov's model
`RMwave` | cardinal sine

Variogram models (stationary increments/intrinsically stationary)

`RMbcw` | bridging model between `RMcauchy` and `RMgenfbm`
`RMdewijsian` | generalised version of the DeWijsian model
`RMgenfbm` | generalized fractal Brownian motion
`RMflatpower` | similar to fractal Brownian motion but always smooth at the origin

General composed models (operators)

Here, composed models are given that can be of any kind (stationary/non-stationary), depending on the submodel.

`RMbernoulli` | Correlation function of a binary field based on a Gaussian field
`RMexponential` | exponential of a covariance model
`RMintexp` | integrated exponential of a covariance model (INCLUDES `ma2`)
`RMpower` | powered variograms
`RMqam` | Porcu's quasi-arithmetric-mean model
`RMS` | details on the optional transformation arguments (`var`, `scale`, `Aniso`, `proj`).

Stationary and isotropic composed models (operators)

`RMcutoff` | Gneiting's modification towards finite range
`RMintrinsic` | Stein's modification towards finite range
`RMnatsc` | practical range
`RMstein` | Stein's modification towards finite range
`RMtbm` | Turning bands operator

Stationary space-time models
See RMmodelsSpaceTime

Non-stationary models
See RMmodelsNonstationary

Negative definite models that are not variograms

`RMsum` | a non-stationary variogram model

Models related to max-stable random fields (tail correlation functions)
See RMmodelsTailCorrelation.

Other covariance models

`RMuser` | User defined model
`RMfixcov` | User defined covariance structure

Trend models

`Aniso` | for space transformation (not really trend, but similiar)
`RMcovariate` | spatial covariates
`RMprod` | to model variability of the variance
`RMpolynome` | easy modelling of polynomial trends
`RMtrend` | for explicite trend modelling
`R.models` | for implicite trend modelling
`R.c` | for multivariate trend modelling

Auxiliary models
See Auxiliary RMmodels.

### Note

- Note that, instead of the named arguments, a single argument `k` can be passed. This is possible if all the arguments are scalar. Then `k` must have a length equal to the number of arguments.

- If an argument equals `NULL` the argument is not set (but must have a valid name).

- `Aniso` can be given also by `RMangle` or any other `RMmodel` instead by a matrix

- Note also that a completely different possibility exists to define a model, namely by a list. This format allows for easy flexible models and modifications (and some few more options, as well as some abbreviations to the model names, see `PrintModelList()`). Here, the argument `var`, `scale`, `Aniso` and `proj` must be passed by the model `RMS`. For instance,

  - `model <- RMexp(scale=2, var=5)`
    is equivalent to
    `model <- list("RMS", scale=2, var=5, list("RMexp"))`
    The latter definition can be also obtained by

    `print(RMexp(scale=2, var=5))`

  - `model <- RMnsst(phi=RMgauss(var=7), psi=RMfbm(alpha=1.5), scale=2, var=5)`
    is equivalent to
    `model <- list("RMS", scale=2, var=5,`
    `list("RMnsst", phi=list("RMS", var=7, list("RMgauss")),`
    `psi=list("RMfbm", alpha=1.5)) )`.

  All models have secondary names that stem from RandomFields versions 2 and earlier and that can also be used as strings in the list notation. See `RFgetModelNames(internal=FALSE)` for the full list.

### Author(s)

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

Martin Schlather, schlather@math.uni-mannheim.de

### 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.

- Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 1-25, url = ‘http://www.jstatsoft.org/v63/i08/’

  ‘multivariate’, the corresponding vignette.

- 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

`RFformula`, RM, `RMmodels`, `RMmodelsAuxiliary`

### Examples

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

    ## a non-stationary field with a sharp boundary of
    ## of the differentiabilities
    x <- seq(-0.6, 0.6, len=50)
    model <- RMwhittle(nu=0.8 + 1.5 * R.is(R.p(new="isotropic"), "<=", 0.5))
    z <- RFsimulate(model=model, x, x, n=4)
    plot(z)

[Package RandomFields version 3.1.50 Index]