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DiggleGatesPointProcess

DiggleGatesPointProcess[μ,ρ,d]

represents a Diggle–Gates point process with constant intensity μ and interaction radius ρ in .

Details

DiggleGatesPointProcess models point configurations where the points have a softcore decreasing repulsive pairwise interaction for points within radius ρ of each other and that are otherwise uniformly distributed.
The Diggle–Gates 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 ρ as follows:
pair potential

$h(r)= sin^2(pi r/(2 rho)) r<rho; 1 TemplateBox[{True, paclet:ref/True}, RefLink, BaseStyle -> {2ColumnTableMod}];$ pair interaction
A point configuration from a Diggle–Gates point process DiggleGatesPointProcess[μ,ρ,d] in an observation region reg has density function proportional to $mu^n product_(i!=j)h(TemplateBox[{{{p, _, i}, -, {p, _, j}}}, Norm])$ , with respect to PoissonPointProcess[1,d].
The Papangelou conditional density for adding a point to a point configuration is $mu product_ih(TemplateBox[{{{p, _, i}, -, q}}, Norm])$ .
DiggleGatesPointProcess allows μ and ρ to be any positive number, and d to be any positive integer.
DiggleGatesPointProcess is a special case of GibbsPointProcess.
DiggleGatesPointProcess simplifies to PoissonPointProcess when .
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 DiggleGatesPointProcess are:
Automatic automatically choose the parameter estimator

"MaximumPseudoLikelihood" maximize the pseudo-likelihood
DiggleGatesPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.