RandomFields (version 3.1.12)

RMmodelsMultivariate: Multivariate models

Description

Here, multivariate and vector-valued covariance models are presented.

Details

Covariance models ll{ RMbiwm full bivariate Whittle-Matern model (stationary and isotropic) RMbigneiting bivariate Gneiting model (stationary and isotropic) RMcurlfree curlfree (spatial) vector-valued field (stationary and anisotropic) RMdelay bivariate delay effect model (stationary) RMdivfree divergence free (spatial) vector valued field, (stationary and anisotropic) RMexponential functional returning $e^C$ RMkolmogorov Kolmogorov's model of turbulence RMmatrix linear model of corregionalisation RMmqam multivariate quasi-arithmetic mean (stationary) RMparswm multivariate Whittle-Matern model (stationary and isotropic) RMschur element-wise product with a positive definite matrix RMtbm turning bands operator RMvector vector-valued field (combining RMcurlfree and RMdivfree) }

Trend models ll{ RMtrend for explicite trend modelling R.models for implicite trend modelling R.c binding univariate trend models into a vector }

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. (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. % \item Schlather, M. (2002) Models for stationary max-stable % random fields. \emph{Extremes} \bold{5}, 33-44.
• Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with packageRandomFields.Journal of Statistical Software,63(8), 1-25, url =http://www.jstatsoft.org/v63/i08/
• Wackernagel, H. (2003)Multivariate Geostatistics.Berlin: Springer, 3rd edition.

See Also

RFformula, RMmodels, RM, RMmodelsAdvanced

../doc/multivariate_jss.pdf{multivariate}, a vignette for multivariate geostatistics

Examples

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

n <- 100
x <- runif(n=n, min=1, max=50)
y <- runif(n=n, min=1, max=50)

rho <- matrix(nc=2, c(1, -0.8, -0.8, 1))
model <- RMparswmX(nudiag=c(0.5, 0.5), rho=rho)

## generation of artifical data
data <- RFsimulate(model = model, x=x, y=y, grid=FALSE)
## introducing some NAs ...
data@data$variable1[1:10] <- NA
data@data$variable2[90:100] <- NA
plot(data)StartExample()
## co-kriging
x <- y <- seq(0, 50, 1)
k <- RFinterpolate(model, x=x, y=y, data= data)
plot(k, data)

## conditional simulation
z <- RFsimulate(model, x=x, y=y, data= data)
plot(z, data)

FinalizeExample()