represents a Strauss point process with constant intensity μ, interaction parameter γ and interaction radius rs in d.
- StraussPointProcess models point configurations with a constant repulsive pairwise interaction for points within radius rs of each other but that are otherwise uniformly distributed.
- The Strauss model is typically used when the process interaction has a constant penalty for points within radius rs, including for locations of plants, birds nests and biological cells.
- The Strauss 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 rs as follows:
pair potential pair interaction
- A point configuration from a Strauss point process StraussPointProcess[μ,γ,rs,d] in an observation region reg has density function proportional to , where with respect to PoissonPointProcess[1,d].
- The Papangelou conditional density for adding a point to a point configuration is where .
- StraussPointProcess allows μ, γ and to be any positive numbers such that , and d to be any positive integer.
- StraussPointProcess simplifies to HardcorePointProcess when and to PoissonPointProcess when . Smaller values of inhibit points being closer than .
- 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 StraussPointProcess are:
Automatic automatically choose the parameter estimator "MaximumPseudoLikelihood" maximize the pseudo-likelihood
- StraussPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (2)
Possible Issues (2)
Wolfram Research (2020), StraussPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/StraussPointProcess.html.
Wolfram Language. 2020. "StraussPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StraussPointProcess.html.
Wolfram Language. (2020). StraussPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StraussPointProcess.html