RandomPointConfiguration

RandomPointConfiguration[pproc,reg]

generates a pseudorandom spatial point configuration from the spatial point process pproc in the observation region reg.

RandomPointConfiguration[pproc,reg, n]

generates an ensemble of n spatial point configurations.

Details and Options

RandomPointConfiguration takes a point process pproc and generates a point configuration as a SpatialPointData object.
RandomPointConfiguration gives a different realization of pseudorandom point configurations whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.
The same process can generate an ensemble consisting of different realizations.
The observation region reg needs to be a parameter-free region, as well as SpatialObservationRegionQ.
The following options can be given:
Method Automatic what method to use

WorkingPrecision MachinePrecision precision used in internal computations
With the setting WorkingPrecisionp, random numbers of precision p will be generated.
Special settings for Method are documented under the individual point process reference pages.
Typical Method settings include:
"MCMC" Markov chain Monte Carlo birth and death

"Thinning" random thinning

"Exact" coupling from the past

Examples

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Basic Examples (2)

Sample from a Poisson point process:

Sample 5 realizations from a binomial point process:

Scope (5)

RandomPointConfiguration returns a SpatialPointData object:

Obtain a list of locations of the points:

Simulate a Strauss point process in a rectangle:

Retrieve points that lie within a unit disk centered at {2,3}:

Visualize points on the plane:

Estimate the parameters for a point process using a simulated point configuration:

Simulate from a Cauchy point process:

Estimate Ripley's function from the sampled point configuration and compare it with the theoretical function:

Simulate an ensemble of 5 realizations over the same region:

Number of points in each realization:

Visualize the distribution of points in different realizations:

Options (3)

Method (2)

Sample from an InhomogeneousPoissonPointProcess using the different methods:

Use the method "Thinning":

Use the Markov chain Monte Carlo method "MCMC":

Visualize samples over the region:

Sample from a Gibbs point process using the Markov chain Monte Carlo method "MCMC" with the number of iterations equal to 30000:

WorkingPrecision (1)

Generate a sample point configuration with default machine precision:

Use WorkingPrecision to generate a sample point configuration with higher precision:

Applications (2)

Estimate the density of a PoissonPointProcess from a sample:

The intensity estimate:

Compare the expected point counts and the average of number of points for an inhomogeneous Poisson point process:

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