Spatial Statistics

Spatial statistics deals with spatial data. There are two fundamentally different views: the first involves a continuous value associated with each spatial point, e.g. temperature, elevation or ozone concentration. In this case, spatial estimation of the value anywhere is a key task. The second view involves the spatial point as an event, e.g. tree location, earthquake location or crime location. In this case, getting statistical measures of center, density and homogeneity of the point locations are key tasks.

The Wolfram Language provides a full suite of tools for spatial statistics, including highly automated spatial estimation for random fields and extensive point pattern analysis and modeling.

Continuous Spatial Estimation »

SpatialEstimate gives a function that can be used to estimate values

VariogramFunction  ▪  SpatialTrendFunction  ▪  SpatialNoiseLevel  ▪  SpatialEstimatorFunction

Spatial Point Collections »

SpatialPointData create and represent spatial point configurations

SpatialRandomnessTest test whether a point configuration is uniformly distributed

Center, Density and Homogeneity Measures

SpatialMedian location in region with minimum distance to all points

Mean  ▪  Median  ▪  CentralFeature  ▪  ...

PointDensity varying point density function

HistogramPointDensity  ▪  SmoothPointDensity  ▪  MeanPointDensity

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

RipleyK  ▪  EmptySpaceF  ▪  PairCorrelationG  ▪  ...

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, Interaction and Clustered Point Processes

PoissonPointProcess constant density of independent points

InhomogeneousPoissonPointProcess  ▪  BinomialPointProcess

HardcorePointProcess constant density of points; no points within radius r of each other

StraussPointProcess  ▪  GibbsPointProcess  ▪  ...

MaternPointProcess constant density of center points, with uniform distribution of cluster points in a disk of radius r around each center

CauchyPointProcess  ▪  NeymanScottPointProcess  ▪  ...