RandomFields (version 3.1.16)

Hierarchical Modelling: Bayesian Spatial Modelling

Description

RandomFields provides Bayesian modelling to some extend: (i) simulation of hierarchical models at arbitrary depth; (ii) estimation of the parameteres of a hierarchical model of depth 1 by means of maximizing the likelihood.

Details

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:

• implicitelty, e.g. RMwhittle(nu=exp()) or
• explicitely 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.

See Also

RMmodelsAdvanced For hierarchical modelling see RR

Examples

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 expontential 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)