represents a Diggle–Gratton point process with constant intensity μ, interaction parameter κ, hard-core interaction radius δ and interaction radius ρ in .
- DiggleGrattonPointProcess is also known as hardcore Diggle process.
- DiggleGrattonPointProcess models point configurations where the points cannot be within a radius δ of each other, have a decreasing repulsive pairwise interaction for points between radius δ and ρ of each other, and are otherwise uniformly distributed.
- The Diggle–Gratton 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 κ, δ and ρ as follows:
pair potential pair interaction
- A point configuration from a Diggle–Gratton point process DiggleGrattonPointProcess[μ,κ,δ,ρ,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 q to a point configuration is .
- DiggleGrattonPointProcess allows μ, κ, δ and ρ to be positive numbers such that , and d to be any positive integer.
- DiggleGrattonPointProcess simplifies to HardcorePointProcess when and to PoissonPointProcess when and . Higher values of make the process more repulsive within radius ρ.
- Possible Method settings in RandomPointConfiguration for DiggleGrattonPointProcess are:
"MCMC" Markov chain Monte Carlo birth and death "Exact" coupling from the past
- Possible PointProcessEstimator settings in EstimatedPointProcess for DiggleGrattonPointProcess are:
Automatic automatically choose the parameter estimator "MaximumPseudoLikelihood" maximize the pseudo-likelihood
- DiggleGrattonPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (2)
Wolfram Research (2020), DiggleGrattonPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/DiggleGrattonPointProcess.html.
Wolfram Language. 2020. "DiggleGrattonPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiggleGrattonPointProcess.html.
Wolfram Language. (2020). DiggleGrattonPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiggleGrattonPointProcess.html