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

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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, see for example GaussRF, MaxStableRF, ect.

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, GaussRF, MaxStableRF

Examples

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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)

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