Description Details Note See Also Examples
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 selfdefined.
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:
implicitly, e.g. RMwhittle(nu=exp())
or
explicitly through RRdistr
, e.g.
RMwhittle(nu=RRdistr(exp()))
.
by use of RRmodels
of the package.
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 maxstable 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.
RMmodelsAdvanced. For hierarchical modelling see RR.
1 2 3 4 5 6 7 8 9 10 11  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 WhittleMatern
## 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)

Loading required package: sp
Loading required package: RandomFieldsUtils
Attaching package: 'RandomFields'
The following object is masked from 'package:RandomFieldsUtils':
RFoptions
Note that behaviour of 'modus_operandi' has changed within 'RFfit' in version 3.1.0 of RandomFields. Roughly:
what was called 'careless' is now called 'sloppy';
what was called 'sloppy' is now called 'easygoing';
what was called 'easygoing' is now called 'normal';
what was called 'normal' is now called 'precise';
etc.
Note that the option 'modus_operandi' is still in an experimental stage, so that the behaviour may change (slightly) in future.
User's variables:
whittle.var whittle.s whittle.nu nugget.var cst
value 4.576851 54.98957 0.3628921 4.572278 11.85625
sd Inf Inf Inf Inf 
#variab loglikelihood AIC
5.0000 497.4614 1004.9227
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