Simulate Log-Gaussian Cox Process
Generate a random point pattern, a realisation of the log-Gaussian Cox process.
rLGCP(model="exp", mu = 0, param = NULL,
...,
win=NULL, saveLambda=TRUE, nsim=1, drop=TRUE)model |
character string: the short name of a covariance model for
the Gaussian random field. After adding the prefix |
mu |
mean function of the Gaussian random field. Either a
single number, a |
param |
List of parameters for the covariance.
Standard arguments are |
... |
Additional parameters for the covariance,
or arguments passed to |
win |
Window in which to simulate the pattern.
An object of class |
saveLambda |
Logical. If |
nsim |
Number of simulated realisations to be generated. |
drop |
Logical. If |
This function generates a realisation of a log-Gaussian Cox process (LGCP). This is a Cox point process in which the logarithm of the random intensity is a Gaussian random field with mean function μ and covariance function c(r). Conditional on the random intensity, the point process is a Poisson process with this intensity.
The string model specifies the covariance
function of the Gaussian random field, and the parameters
of the covariance are determined by param and ....
To determine the covariance model, the string model
is prefixed by "RM", and a function of this name is
sought in the RandomFields package.
For a list of available models see
RMmodel in the
RandomFields package. For example the
Matern covariance is specified by model="matern", corresponding
to the function RMmatern in the RandomFields package.
Standard variance parameters (for all functions beginning with
"RM" in the RandomFields package) are var
for the variance at distance zero, and scale for the scale
parameter. Other parameters are specified in the help files
for the individual functions beginning with "RM". For example
the help file for RMmatern states that nu is a parameter
for this model.
This algorithm uses the function RFsimulate in the
RandomFields package to generate values of
a Gaussian random field, with the specified mean function mu
and the covariance specified by the arguments model and
param, on the points of a regular grid. The exponential
of this random field is taken as the intensity of a Poisson point
process, and a realisation of the Poisson process is then generated by the
function rpoispp in the spatstat package.
If the simulation window win is missing or NULL,
then it defaults to
Window(mu) if mu is a pixel image,
and it defaults to the unit square otherwise.
The LGCP model can be fitted to data using kppm.
A point pattern (object of class "ppp")
or a list of point patterns.
Additionally, the simulated intensity function for each point pattern is
returned as an attribute "Lambda" of the point pattern,
if saveLambda=TRUE.
Abdollah Jalilian and Rasmus Waagepetersen. Modified by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Moller, J., Syversveen, A. and Waagepetersen, R. (1998) Log Gaussian Cox Processes. Scandinavian Journal of Statistics 25, 451–482.
if(require(RandomFields)) {
# homogeneous LGCP with exponential covariance function
X <- rLGCP("exp", 3, var=0.2, scale=.1)
# inhomogeneous LGCP with Gaussian covariance function
m <- as.im(function(x, y){5 - 1.5 * (x - 0.5)^2 + 2 * (y - 0.5)^2}, W=owin())
X <- rLGCP("gauss", m, var=0.15, scale =0.5)
plot(attr(X, "Lambda"))
points(X)
# inhomogeneous LGCP with Matern covariance function
X <- rLGCP("matern", function(x, y){ 1 - 0.4 * x},
var=2, scale=0.7, nu=0.5,
win = owin(c(0, 10), c(0, 10)))
plot(X)
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