RMmodelsMultivariate: Multivariate models
In RandomFields: Simulation and Analysis of Random Fields

Description Details References See Also Examples

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

Bivariate covariance models

`RMbicauchy`	a bivariate Cauchy model
`RMbiwm`	full bivariate Whittle-Matern model (stationary and isotropic)
`RMbigneiting`	bivariate Gneiting model (stationary and isotropic)
`RMbistable`	a bivariate stable model

Physically motivated, vector valued covariance and variogram models

`RMcurlfree`	curlfree (spatial) vector-valued field (stationary and anisotropic)
`RMdivfree`	divergence free (spatial) vector-valued field (stationary and anisotropic)
`RMkolmogorov`	Kolmogorov's model of turbulence
`RMvector`	vector-valued field (combining `RMcurlfree` and `RMdivfree`)

Multivariate covariance models

`RMdelay`	delay effect model (stationary)
`RMderiv`	field and its gradient
`RMmatrix`	linear model of coregionalization
`RMparswm`	multivariate Whittle-Matern model (stationary and isotropic)

Operators

`RMcov`	covariance structure given by a multivariate variogram
`RMexponential`	functional returning exp(C)
`RMmatrix`	linear model of coregionalization
`RMmqam`	multivariate quasi-arithmetic mean (stationary)
`RMschur`	element-wise product with a positive definite matrix
`RMtbm`	turning bands operator

Trend models

`RMtrend`	for explicit trend modelling
`R.models`	for implicit trend modelling
`R.c`	binding univariate trend models into a vector

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.
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/’
Wackernagel, H. (2003) Multivariate Geostatistics. Berlin: Springer, 3rd edition.

RFformula, RMmodels, RM, RMmodelsAdvanced

‘multivariate’, a vignette for multivariate geostatistics

 
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
dta <- RFsimulate(model = model, x=x, y=y, grid=FALSE)

## introducing some NAs ...
dta@data$variable1[1:10] <- NA
if (interactive()) dta@data$variable2[90:100] <- NA

plot(dta)


## co-kriging
x <- y <- seq(0, 50, 1)

k <- RFinterpolate(model, x=x, y=y, data= dta)
plot(k, dta)

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