Bayesian Spatial Modelling
RandomFields provides Bayesian modelling to some extend: (i) simulation of hierarchical models at arbitrary depth; (ii) estimation of the parameters of a hierarchical model of depth 1 by means of maximizing the likelihood.
A Bayesian approach can be taken for scalar, real valued model
parameters, e.g. the shape parameter nu in the
RMmatern model.
A random parameter can be passed through a distribution
of an existing family, e.g. (dnorm, pnorm,
qnorm, rnorm) or self-defined.
It is passed without the leading letter
d, p, q, r, but as a function call
e.g norm().
This function call may contain arguments that must be
named, e.g. norm(mean=3, sd=5).
Usage:
exp() denotes the exponential distribution family
with rate 1,
exp(3) is just the scalar e^3 and
exp(rate=3) is the exponential
distribution family with rate 3.
The family can be passed in three ways:
The first is more convenient, the second more flexible and slightly safer.
While simulating any depth of hierarchical modelling is possible, estimation is currently restricted to one level of hierarchy.
The effect of the distribution family varies between the different processes:
in max-stable fields and
RPpoisson, a new realization of the prior
distribution(s) is drawn for each shape function
in all other cases: a realization of the prior(s)
is only drawn once.
This effects, in particular, Gaussian fields with argument
n>1, where all realizations are based on the same
realization out of the prior distribution(s).
Note that checking the validity of the arguments is rather limited for such complicated models, in general.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
RMmodelsAdvanced. For hierarchical modelling see RR.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again ## See 'RRmodels' for hierarchical models ## the following model defines the argument nu of the Whittle-Matern ## model to be an exponential random variable with rate 5. model <- ~ 1 + RMwhittle(scale=NA, var=NA, nu=exp(rate=5)) + RMnugget(var=NA) data(soil) fit <- RFfit(model, x=soil$x, y=soil$y, data=soil$moisture, modus="careless") print(fit)
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