represents a hard-core point process with constant intensity μ and hard-core radius rh in .
- HardcorePointProcess models point configurations where the points cannot be within a radius rh of each other but otherwise are uniformly distributed with intensity μ points per volume unit.
- The hard-core model is typically used when the underlying points behave like a collection of hard marbles, including things like gas molecules, metal deposits, sintered material and biological cells.
- The hard-core point process can be defined as a GibbsPointProcess in terms of its intensity μ and the pair potential or pair interaction , which are both parametrized by rh as follows:
pair potential pair interaction
- A point configuration from a hard-core point process HardcorePointProcess[μ,rh,d] 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 .
- HardcorePointProcess allows μ and rh to be any positive numbers, and d to be any positive integer.
- HardcorePointProcess is a special case of GibbsPointProcess and is equivalent to StraussPointProcess[μ, 0, rh].
- Possible Method settings in RandomPointConfiguration for HardcorePointProcess are:
"MCMC" MCMC birth and death "Exact" coupling from the past
- Possible PointProcessEstimator settings in EstimatedPointProcess for HardcorePointProcess are:
Automatic automatically choose the parameter estimator "MaximumPseudoLikelihood" maximize the pseudo-likelihood
- HardcorePointProcess can be used with such functions as RipleyK and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (2)
Properties & Relations (3)
Wolfram Research (2020), HardcorePointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/HardcorePointProcess.html.
Wolfram Language. 2020. "HardcorePointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HardcorePointProcess.html.
Wolfram Language. (2020). HardcorePointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HardcorePointProcess.html