Spatial Statistics

Spatial point configurations are collections of points (or events) in space. Examples include the location of trees in a forest, the location of gold deposits, the location of stars, the location of earthquakes, crime locations, animal sightings, etc. Often the objective is to quantify trends in the density of points, presence clustering or regularity and to give models that can generate similar point patterns. Spatial point pattern and point process analysis is used in ecology, epidemiology, geoscience, astronomy, econometrics and crime research, etc.  The Wolfram Language provides a complete toolkit for working with spatial point patterns and point processes, from exploratory analysis with visualization and descriptive statistics to modeling and simulation.

Spatial Point Collections »

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

RandomPointConfiguration simulate a point process to give a point collection

Location Measures

Mean  ▪  SpatialMedian  ▪  CentralFeature

Density Measures

MeanPointDensity average number of points per area, volume, etc.

PointDensity varying point density function

HistogramPointDensity  ▪  SmoothPointDensity  ▪  PointDensityFunction

Counting Measures

PointCountDistribution the distribution of point counts for any region

Homogeneity Measures »

RipleyK expected number of points within distance r of each point

EmptySpaceF probability of finding another point within distance r of any location

NearestNeighborG probability of finding another point within distance r of a point

PairCorrelationG probability density of finding another point at distance of a point

BesagL  ▪  SpatialJ  ▪  ...

Hypothesis Tests

SpatialRandomnessTest test whether data is uniformly distributed

PointProcessFitTest test whether data follows a point process

Spatial Point Processes »

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

Independent Point Processes

PoissonPointProcess constant intensity

InhomogeneousPoissonPointProcess varying intensity

BinomialPointProcess uniform distribution of 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