Parsimonious Multivariate Whittle Matern Model
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.
RMparswm(nudiag, var, scale, Aniso, proj) RMparswmX(nudiag, rho, var, scale, Aniso, proj)
nudiag |
a vector of arbitrary length of positive values; the vector (ν_{11},ν_{22},...). The offdiagonal elements ν_{ij} are calculated as 0.5 (ν_{ii} + ν_{jj}). |
rho |
any positive definite m x m
matrix;
here, m equals |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
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)).
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Gneiting, T., Kleiber, W., Schlather, M. (2010) Matern covariance functions for multivariate random fields JASA
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) plot(model) x.seq <- y.seq <- seq(-10, 10, 0.1) z <- RFsimulate(model = model, x=x.seq, y=y.seq) plot(z)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.