PenttinenPointProcess
PenttinenPointProcess[μ,γ,rp,d]
represents a Penttinen point process with constant intensity μ, interaction parameter γ and interaction radius rp in .
Details
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- 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.
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Examples
open allclose allBasic Examples (2)
Scope (2)
Options (3)
Wolfram Research (2020), PenttinenPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
Text
Wolfram Research (2020), PenttinenPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
CMS
Wolfram Language. 2020. "PenttinenPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
APA
Wolfram Language. (2020). PenttinenPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PenttinenPointProcess.html