Parsimonious Multivariate Whittle Matern Model

Description

RMparswm is a multivariate stationary isotropic covariance model whose corresponding covariance function only depends on the distance r ≥ 0 between two points and is given for i,j = 1,2 by

C_{ij}(r)=c_{ij} W_{ν_{ij}}(r).

Here W_ν is the covariance of the RMwhittle model.

RMparswmX ist defined as

ρ_{ij} C_{ij}(r)

where ρ_{ij} is any covariance matrix.

Usage

RMparswm(nudiag, var, scale, Aniso, proj)
RMparswmX(nudiag, rho, var, scale, Aniso, proj)

Arguments

Details

In the equation above we have

c_{ij} = ρ_{ ij} √ G_{ij}

and

G_{ij} = Γ(ν_{11} + d/2) Γ(ν_{22} + d/2) Γ(ν_{12}) / (Γ(ν_{11}) Γ(ν_{22}) Γ(ν_{12}+d/2))^2)

where Γ is the Gamma function and d is the dimension of the space.

Note that the definition of RMparswmX is RMschur(M=rho, RMparswm(nudiag, var, scale, Aniso, proj)) .

Value

RMparswm returns an object of class RMmodel

Author(s)

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

References

• Gneiting, T., Kleiber, W., Schlather, M. (2010) Matern covariance functions for multivariate random fields JASA

See Also

RMbiwm, RMwhittle, RMmodel, RFsimulate, RFfit.

Examples

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


rho <- matrix(nc=3, c(1, 0.5, 0.2, 0.5, 1, 0.6, 0.2, 0.6, 1))
model <- RMparswmX(nudiag=c(1.3, 0.7, 2), rho=rho)
x.seq <- y.seq <- seq(-10, 10, 0.1)
z <- RFsimulate(model = model, x=x.seq, y=y.seq)
plot(z)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RandomFields)
Loading required package: sp
Loading required package: RandomFieldsUtils
This is RandomFieldsUtils Version: 0.2.1
This is RandomFields Version: 3.1.16

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/RandomFields/RMparswm.Rd_%03d_medium.png", width=480, height=480)
> ### Name: RMparswm
> ### Title: Parsimonious Multivariate Whittle Matern Model
> ### Aliases: RMparswm RMparswmX
> ### Keywords: spatial models
> 
> ### ** Examples
> 
> 
> RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
> ##                   RFoptions(seed=NA) to make them all random again
> ## Don't show: 
> StartExample()
> ## End(Don't show)
> 
> rho <- matrix(nc=3, c(1, 0.5, 0.2, 0.5, 1, 0.6, 0.2, 0.6, 1))
> model <- RMparswmX(nudiag=c(1.3, 0.7, 2), rho=rho)
> x.seq <- y.seq <- seq(-10, 10, 0.1)
> z <- RFsimulate(model = model, x=x.seq, y=y.seq)
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.
> plot(z)
> 
> ## Don't show: 
> FinalizeExample()
> ## End(Don't show)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>