RandomFields (version 3.1.16)

RMmodelsMultivariate: Multivariate models

Description

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

Details

Covariance models

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 $exp(C)$

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

Trend models

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.
• 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.

See Also

RFformula, RMmodels, RM, RMmodelsAdvanced

‘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)



## 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)