sim_nsppp: Generation of a realisation of a Neyman-Scott process

Description

This algorithm generates a realisation of a Neyman-Scott process whose expected number of points equals the number of observations in a given pattern.

Usage

sim_nsppp(ppdata, radius, clustering = 5, thinning = 0)

Value

The simulated point pattern (an object of class "ppp"). Additionally, some intermediate results of the simulation are returned as attributes of this point pattern: see rNeymanScott.

Arguments

ppdata: observed point pattern, whose estimated intensity (adjusted for thinning and divided by "clustering") is used for simulating the parent process
radius: radius of the circles around the parent points in which the cluster points are located (Maximum radius of a random cluster)
clustering: a value larger or equal 1 which describes the amount of clustering; the adjusted estimated intensity of the observed pattern is divided by this value; it is also the parameter of the Poisson distribution for the number of points per cluster
thinning: constant thinning probability (in case the observed pattern is a thinned version of a full pattern); usually equal to the probability of having unobserved events

Details

First, the algorithm generates a Poisson point process (see rpoispp for details) of parent points with intensity kappa, which is a pixel image object of class "im" (see im.object).
This pixel image is derived from the observed pattern using density.ppp. The bandwidth is not chosen in advance.
If only a thinned version of the original pattern has been observed, this can be taken into account using the parameter thinning. Usually, not the estimated intensity itself is used for simulating the parent process, but its values are divided by a constant named "clustering".
Second, each parent point is replaced by a random cluster of points, created by calling the function runifdisc. Each cluster consists of a Poisson distributed number of points (with clustering being the expected number of points in each cluster) which are located in a disc of a given radius. These clusters are combined to yield a single point pattern which is then returned as the result.
The estimation of the intensity (on an adequate window) and the simulation of the Neyman-Scott process are performed seperately, so the intensity does not need to be reestimated in every iteration.
The resulting process is a Mat?rn process whose parent process is an inhomogeneous Poisson point process.

Examples

Run this code

if (FALSE) {      
 data(craterA)
 data(craterB)
 set.seed(100)
 sim_pp1 <- sim_nsppp(craterA, radius=300, clustering=15, thinning=0.1)
 sim_pp2 <- sim_nsppp(craterB, radius=300, clustering=15, thinning=0.1)
 op <- par(mfrow = c(1, 2))
 plot(sim_pp1, main = "simulated cluster process 1")
 plot(sim_pp2, main = "simulated cluster process 2")
 par(op)
 }