R: Distribution families (RR commands)

Distribution Families {RandomFields} | R Documentation

## Distribution families (RR commands)

### Description

Distribution families to specify random parameters in the model definition.

### Details

See Bayesian Modelling for some less technical introduction to hierarchical modelling.

When simulating Gaussian random fields, the random parameters are drawn only once at the very beginning. So, if the argument `n` in `RFsimulate` is greater than `1` then `n` simulations conditional on a single realisation of the random parameters are performed. See the examples below.

There are (simple) multivariate version and additional version to the distributions families implemented. Further, any distribution family defined in R can be used, see the examples below

These function will allow for Bayesian modelling. (Future project).

### Implemented models

`RRdeterm` | no scattering
`RRdistr` | families of distributions transferred from R
`RRgauss` | a (multivariate) Gaussian random variable
`RRloc` | modification of location and scale
`RRspheric` | random scale for the `RMball` to simulate `RMspheric`, etc.
`RRunif` | a (multivariate) uniform random variable

### Note

The allowance of random parameters is a very recent, developing feature of RandomField.

Future changings of the behaviour are not unlikely.

### Note

A further random element is `RMsign`, which is an operator on shape functions. As an exception its name starts with `RM` and not with `RR`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### See Also

RC, RF, RM, RP, R. `Other models`, `RFdistr`, `RMmodelgenerator`,

### Examples

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

    ## here, the scale is given by an exponential variable:
    model <- RMgauss(scale=exp())
    for (i in 1:4) {
      RFoptions(seed = i)
      # each leads to a simulation with a different scale parameter
      plot(model) ## random
      plot(RFsimulate(model, x=seq(0,10,0.1)))
      readline("press return")
    }

    # but here, all 4 simulations have same (but random) scale:
    plot(RFsimulate(model, x=seq(0,10,0.1), n=4))

    ## hierarchical models are also possible:
    ## here, the scale is given by an exponential variable whose
    ## rate is given by a uniform variable
    model <- RMgauss(scale=exp(rate=unif()))
    plot(model)
    plot(RFsimulate(model, x=seq(0,10,0.1)))

    ## HOWEVER, the next model is deterministic with scale \eqn{e=2.718282}.
    model <- RMgauss(scale=exp(1))
    plot(model)
    plot(RFsimulate(model, x=seq(0,10,0.1)))

[Package RandomFields version 3.1.50 Index]