RFsim {CompRandFld}R Documentation

Simulation of Gaussian, Binary and Max-stable Random Fields

Description

Simulation of spatial and spatio-temporal Gaussian, binary and max-stable random fields. The function returns one or more replications of a random field for a given covariance model and covariance parameters.

Usage

RFsim(coordx, coordy=NULL, coordt=NULL, corrmodel, distance="Eucl",
      grid=FALSE, model='Gaussian', numblock=NULL, param,
      replicates=1, threshold=NULL)

Arguments

coordx

A numeric (d x 2)-matrix (where d is the number of spatial sites) giving 2-dimensions of spatial coordinates or a numeric d-dimensional vector giving 1-dimension of spatial coordinates.

coordy

A numeric vector giving 1-dimension of spatial coordinates; coordy is interpreted only if coordx is a numeric vector or grid=TRUE otherwise it will be ignored. Optional argument, the default is NULL then coordx is expected to be numeric a (d x 2)-matrix.

coordt

A numeric vector giving 1-dimension of temporal coordinates. At the moment implemented only for the Gaussian case. Optional argument, the default is NULL then a spatial random field is expected.

corrmodel

String; the name of a correlation model, for the description see the Section Details.

distance

String; the name of the spatial distance. The default is Eucl, the euclidean distance. See the Section Details of FitComposite.

grid

Logical; if FALSE (the default) the data are interpreted as spatial or spatial-temporal realisations on a set of non-equispaced spatial sites (irregular grid).

model

String; the type of random field and therefore the densities associated to the likelihood objects. Gaussian is the default, see the Section Details.

numblock

Numeric; the observation size of the underlying random field. Only in case of max-stable random fields.

param

A list of parameter values required in the simulation procedure of random fields, see Examples.

replicates

Numeric; a positive integer denoting the number of independent and identically distributed (iid) replications of a spatial or spatial-temporal random field. Optional argument, the default value is 1 then a single realisation is considered.

threshold

Numeric; a value indicating a threshold for the binary random field. Optional in the case that model is BinaryGauss, see the Section Details.

Details

Note that this function is also interfaced to the R package RandomFields, using fast routines therein developed for the simulation of random fields.

Value

Returns an object of class RFsim. An object of class RFsim is a list containing at most the following components:

coordx

A d-dimensional vector of spatial coordinates;

coordy

A d-dimensional vector of spatial coordinates;

coordt

A t-dimensional vector of temporal coordinates;

corrmodel

The correlation model; see Covmatrix.

data

The vector or matrix or array of data, see FitComposite;

distance

The type of spatial distance;

model

The type of random field, see FitComposite.

numcoord

The number of spatial coordinates;

numtime

The number the temporal realisations of the random field;

param

The vector of parameters' estimates;

randseed

The seed used for the random simulation;

replicates

The number of the iid replicatations of the random field;

spacetime

TRUE if spatio-temporal and FALSE if spatial random field;

threshold

The threshold for deriving the binary random field.

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, http://faculty.unibocconi.it/simonepadoan; Moreno Bevilacqua, moreno.bevilacqua@uv.cl, https://sites.google.com/a/uv.cl/moreno-bevilacqua/home.

References

Padoan, S. A. and Bevilacqua, M. (2015). Analysis of Random Fields Using CompRandFld. Journal of Statistical Software, 63(9), 1–27.

See Also

Covmatrix

Examples

library(CompRandFld)
library(RandomFields)
library(mapproj)
library(fields)

################################################################
###
### Example 1. Simulation of a Gaussian random field.
### Gaussian random fields with Whittle-Matern correlation.
### One spatial replication.
###
###
###############################################################

# Define the spatial-coordinates of the points:
x <- runif(500, 0, 2)
y <- runif(500, 0, 2)

set.seed(261)
# Simulation of a spatial Gaussian random field:
data <- RFsim(x, y, corrmodel="matern", param=list(smooth=0.5,
             mean=0,sill=1,scale=0.2,nugget=0))$data

################################################################
###
### Example 2. Simulation of a binary random field based on
### the latent Gaussian random field with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################

# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.05)
y <- seq(0, 1, 0.05)

set.seed(251)

# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE,
             model="BinaryGauss", threshold=0,
             param=list(nugget=0,mean=0,scale=.1,sill=1))

image(x,y,sim$data,col=terrain.colors(100))

################################################################
###
### Example 3. Simulation of a max-stable random
### extremal-t type with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################

set.seed(341)
x <- seq(0, 1, 0.02)
y <- seq(0, 1, 0.02)
# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE, model="ExtT",
             numblock=500, param=list(nugget=0,mean=0,scale=.1,
             sill=1,df=5))

image.plot(x,y,log(sim$data))


################################################################
###
### Example 4. Simulation of a Gaussian random field.
### with double exponential correlation.
### One spatio-temporal replication.
###
###
###############################################################

# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.1)
y <- seq(0, 1, 0.1)
# Define the temporal-coordinates:
times <- seq(1, 3, 1)
#
# Simulation of a spatial Gaussian random field:
sim <- RFsim(x, y, times, corrmodel="exp_exp", grid=TRUE,
             param=list(nugget=0,mean=0,scale_s=0.3,
             scale_t=0.5,sill=1))$data
# Spatial simulated data at first temporal instant
 sim[,,1]




################################################################
###
### Example 5. Simulation of a Gaussian random field
### with  exponential correlation on a portion of  the earth surface
### One spatial replication.
###
###
###############################################################

lon_region<-c(-40,40)
lat_region<-c(-40,40)
#
lon<-seq(min(lon_region),max(lon_region),2)
lat<-seq(min(lat_region),max(lat_region),2)
#
data<-RFsim(coordx=lon,coordy=lat,corrmodel="exponential",
         distance="Geod",grid=TRUE,param=list(nugget=0,mean=0
         ,scale=8000,sill=1))$data
image.plot(lon,lat,data,xlab="Longitude",ylab="Latitude")
map(database="world",xlim=lon_region,ylim=lat_region,add=TRUE)

[Package CompRandFld version 1.0.3-6 Index]