Spatial Point Processes

Spatial point processes are models for spatial point configurations. They can be used to generate random point configurations following that model. This is often useful for generating data or designs such as a Poisson forest. Conversely, given point data, the best-fitting point process that could have generated that data can be estimated. This give close coupling between data and models.  The Wolfram Language provides a rich collection of point process models, which, together with random sampling and estimation, provides deep integration into the rest of spatial statistics, geometry, geography and visualization.

Simulation, Estimation and Testing

RandomPointConfiguration simulate a point process to give a point collection

EstimatedPointProcess estimate a point process from spatial point configurations

PointProcessFitTest test whether data follows a point process

PointCountDistribution give the distribution of point counts for a region

FindPointProcessParameters  ▪  PointProcessParameterQ  ▪  PointProcessEstimator  ▪  PointProcessParameterAssumptions

Spatial Point Data and Statistics »

SpatialPointData create and represent spatial point data with observation region

SpatialBinnedPointData create and represent aggregated point data with any region partition

ResourceData spatial point datasets from a variety of sources

MeanPointDensity  ▪  PointDensity  ▪  RipleyK  ▪  EmptySpaceF  ▪  ...

Independent Point Processes

PoissonPointProcess constant intensity

InhomogeneousPoissonPointProcess varying intensity

BinomialPointProcess uniform distribution of n points

Interaction Point Processes

HardcorePointProcess hard-core with no point interaction within radius

StraussPointProcess soft-core with limited point interaction within radius

StraussHardcorePointProcess hard-core limited point interaction between two radii

PenttinenPointProcess strength of interaction based on overlapping disk area

DiggleGrattonPointProcess hard-core interaction with a gradual transition

DiggleGatesPointProcess gradual hard-core to soft-core interaction

GibbsPointProcess completely general point interaction

Clustered Point Processes

MaternPointProcess cluster process with uniform (daughter) pattern in disk (isotropic)

ThomasPointProcess cluster process with normal (daughter) pattern (isotropic)

CauchyPointProcess cluster process with heavy (daughter) pattern (isotropic)

VarianceGammaPointProcess cluster process with variance-gamma (daughter) pattern (isotropic)

NeymanScottPointProcess general cluster process with inhomogeneous base point process and general point process as daughter process