Multivariate models
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
Operators
Trend models
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
‘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)
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