RMSadvanced: Scaling operator - comments for advanced applications
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

Here advances uses are given for the arguments var, scale, Aniso, proj that are available to most of the models

RMS(phi, var, scale, Aniso, proj, anisoT)

phi

submodel

var

Instead of a constant it can be also an arbitrary non-negative function, see R. and RMuser for defining arbitrary functions.

scale

instead of a positive constant it can be an arbitrary, positive deterministic function. In case of the latter, the scale should be given by one of the functions RMbubble or RMscale. In case none of them are given, RMscale is assumed with scale penality \|s(x) - s(y)\|^2 for the square of the norm.

The scale can be also a random variable in case of Bayesian modelling.

Aniso

matrix or RMmodel. Instead of a matrix, Aniso can be an arbitrary, vector-valued function .

proj

is the optional projection vector which defines a diagonal matrix of zeros and ones and proj gives the positions of the ones (integer values between 1 and the dimension of x). It also allows for the values 'space' and 'time' in case of space-time modelling.

anisoT

the transpose of the anisotropy matrix B, multiplied from the left by a distance vector x, i.e. x^\top B.

See the reference for Gneitings nsst model used for modelling scales. See also the example below.

RMSadvanced returns an object of class RMmodel.

Bonat, W.H. , Ribeiro, P. Jr. and Schlather, M. (2019) Modelling non-stationarity in scale. In preparation.

RMS, RMblend for a different approach on modelling different scales

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

x <- seq(0,1, if (interactive()) 0.01 else 0.5)
d <- sqrt(rowSums(as.matrix(expand.grid(x-0.5, x-0.5))^2))
d <- matrix(d < 0.25, nc=length(x))
image(d)

scale <- RMcovariate(data=as.double(d) * 2 + 0.5, raw=TRUE)

S <- RMexp(scale = scale)
plot(zS <- RFsimulate(S, x, x))
CS <- RFcovmatrix(S, x, x)