represents a Penttinen point process with constant intensity μ, interaction parameter γ and interaction radius rp in .
- PenttinenPointProcess is also known as pairwise area interaction process.
- PenttinenPointProcess models point configurations where points have a pairwise repulsion that is log-linear in the measure of the overlap between balls around the points of radius rp, which are otherwise uniformly distributed.
- The Penttinen model is typically used when the process interaction depends on the amount of shared resources within radius rp, such as plants, trees and nests of animals.
- The Penttinen point process can be defined as a GibbsPointProcess in terms of its intensity μ and the pair potential ϕ or pair interaction h, which are both parametrized by γ and rp as follows:
pair potential pair interaction
- Here is the measure of overlapping balls:
overlapping area in overlapping volume in overlapping measure in
- A point configuration from a Penttinen point process in an observation region reg has density function proportional to , with respect to PoissonPointProcess[1,d].
- The Papangelou conditional density for adding a point to a point configuration is .
- PenttinenPointProcess allows μ, γ and rp to be positive numbers such that , and d to be any positive integer.
- PenttinenPointProcess simplifies to PoissonPointProcess when . Smaller values of inhibit points within .
- Possible Method settings in RandomPointConfiguration for StraussPointProcess are:
"MCMC" Markov chain Monte Carlo birth and death "Exact" coupling from the past
- Possible PointProcessEstimator settings in EstimatedPointProcess for PenttinenPointProcess are:
Automatic automatically choose the parameter estimator "MaximumPseudoLikelihood" maximize the pseudo-likelihood
- PenttinenPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (2)
Wolfram Research (2020), PenttinenPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
Wolfram Language. 2020. "PenttinenPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
Wolfram Language. (2020). PenttinenPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PenttinenPointProcess.html