StraussHardcorePointProcess

StraussHardcorePointProcess[μ,γ,rh,rs,d]

represents a Strauss hardcore point process with constant intensity μ, interaction parameter γ, hard-core interaction radius rh and Strauss interaction radius rs in .

Details

  • StraussHardcorePointProcess models point configurations where the points cannot be within a hardcore radius r_(h) of each other, have a constant repulsive pairwise interaction for points within between radius r_(h) and r_(s) of each other, and which are otherwise uniformly distributed.
  • The Strauss hardcore model is typically used to model point processes like trees in a forest, where the r_(h) and r_(s) correspond to the trunk and canopy radius, respectively.
  •     
  • The Strauss hardcore 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 γ, rh and rs as follows:
  • pair potential
    pair interaction
  • A point configuration from a Strauss hardcore point process 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]).
  • StraussHardcorePointProcess allows μ, γ, rh and rs to be positive numbers such that , and d to be any positive integer.
  • StraussHardcorePointProcess simplifies to HardcorePointProcess when , or . Smaller values of gamma inhibit points being closer than r_(s).
  • 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 StraussHardcorePointProcess are:
  • Automaticautomatically choose the parameter estimator
    "MaximumPseudoLikelihood"maximize the pseudo-likelihood
  • StraussHardcorePointProcess can be used with such functions as RipleyK and RandomPointConfiguration.

Examples

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Basic Examples  (2)

Sample from a Strauss hardcore point process:

Visualize the points in the sample:

Sample from a geo region:

Visualize the points:

Scope  (5)

Generate three realizations from a Strauss hardcore point process:

Estimate the parameters:

Generate three realizations from a Strauss hardcore point process in the geo region:

Visualize the point configurations:

Estimate the parameters:

Generate samples with increasing hardcore radius:

Generate samples with increasing Strauss radius:

Generate samples with increasing interacting parameter γ:

Options  (4)

Method  (4)

Simulate using the Markov chain Monte Carlo method:

Specify the number of recursive calls to the sampler:

Specify the length of run:

Provide an initial state for the simulation:

Provide an initial state for the simulation:

The initial state must have nonzero density to ensure that the result does:

Check if the minimal distance between the points is smaller than the hardcore radius:

Sample using an exact method:

Visualize the points in the sample:

Possible Issues  (1)

By default, the simulation will run until the number of points converges to a steady state, or until the default number of iterations is reached:

Raise the number of recursive calls to the sampler:

Increase the length of run:

Wolfram Research (2020), StraussHardcorePointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html.

Text

Wolfram Research (2020), StraussHardcorePointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html.

BibTeX

@misc{reference.wolfram_2020_strausshardcorepointprocess, author="Wolfram Research", title="{StraussHardcorePointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html}", note=[Accessed: 17-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_strausshardcorepointprocess, organization={Wolfram Research}, title={StraussHardcorePointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html}, note=[Accessed: 17-January-2021 ]}

CMS

Wolfram Language. 2020. "StraussHardcorePointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html.

APA

Wolfram Language. (2020). StraussHardcorePointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StraussHardcorePointProcess.html