RandomFields (version 3.1.12)

RMmodel: 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. %Argument %corresponding to specific covariance model
• varis the optional variance argument$v$,
• scalethe optional scale argument$s$,
• Anisoan optional anisotropy matrix$A$or given byRMangle, and
• projis the optional projection vector which defines a diagonal matrix of zeros and ones andprojgives the positions of the ones (integer values). In a space-time framework, also"space"and"time"are valid values.

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

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 ll{ 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)

ll{ RMfbm fractal Brownian motion }

Basic Operations

ll{ RMmult, * product of covariance models RMplus, + sum of covariance models or variograms }

Basic models for mixed effect modelling ll{ 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 ll{ RMtrend trend RMangle defines a 2x2 anisotropy matrix by rotation and stretch arguments. }

References

• Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley. % \item Gneiting, T. and Schlather, M. (2004) % Statistical modeling with covariance functions. % \emph{In preparation.}
• 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)

FinalizeExample()