Scaling operator – comments for advanced applications
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)
submodel
Instead of a constant it can be
also an arbitrary non-negative function, see R.
and RMuser for defining arbitrary functions.
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.
matrix or RMmodel.
Instead of a matrix, Aniso can be an arbitrary, vector-valued
function .
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.
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.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Bonat, W.H. , Ribeiro, P. Jr. and Schlather, M. (2019) Modelling non-stationarity in scale. In preparation.
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)
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