R: Multivariate models

RMmodelsMultivariate {RandomFields} | R Documentation

## Multivariate models

### Description

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

### Details

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
`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
`RMvector` | vector-valued field (combining `RMcurlfree` and `RMdivfree`)

Trend models

`RMtrend` | for explicite trend modelling
`R.models` | for implicite trend modelling
`R.c` | binding univariate trend models into a vector

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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)

[Package RandomFields version 3.1.50 Index]