线性网络上泊松聚类过程的模拟

Question

On pp. 73-74 in "“Stationary” point processes are uncommon on linear networks" * by Adrian Baddeley, Gopolan Nair, Suman Rakshit, and Greg McSwiggan, the authors introduce a Poisson cluster process on a linear network and subsequently demonstrate a simulation.

Unfortunately, I cannot find related code. Does {spatstat} provide an algorithm to simulate such a process?

On pp. 24-25 in "Analysing point patterns on networks — A review" * by the aforementioned authors and Tilman M. Davies one can read:

"Point process models which exhibit clustering (positive association between points), such as Poisson cluster processes and Cox processes [...], can easily be constructed on a linear network, [...]".

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*You need sth. like an academic vpn to view and download the pdf without any expense.

Answer 1

It would be easier to ask the authors directly.

Here is some code (written by Greg McSwiggan) to generate a Thomas cluster process on a network.

rThomaslpp <- function(L, kappa, mu, sigma) {
 X <- rpoislpp(kappa, L)
 Y <- density(X, sigma)
 Y <- eval.linim(Y * mu)
 Z <- rpoislpp(Y, L)
 return(Z)
}

The network is L . The parent intensity is kappa (points per unit length), the mean number of offspring per parent is mu (dimensionless), and the cluster size is sigma (length units).

Example:

require(spatstat)
X <- rThomaslpp(simplenet, 4, 6, 0.07)
plot(X)

This code will be added to the next version of the package spatstat.linnet .