Overview of spatstat

The package supports

Point patterns

The window of observation for the point pattern may have arbitrary shape (represented by a rectangle, a binary image mask, a polygon, or several polygons, with or without holes).

The points of the pattern may have "marks", that is, extra data attached to them.

Exploratory data analysis

The package implements many standard summary statistics for point patterns, including Ripley's K-function, the inhomogeneous K-function, the empty space function F, the nearest neighbour function G, the J-function, the pair correlation function, and counterparts of these functions for the case of multitype point patterns. It also includes the mark correlation function.

Stochastic Simulation

Various simulation algorithms are implemented, including naive methods based on the Poisson process, and a Metropolis-Hastings birth-death algorithm.

Parametric model-fitting

Point process models can be fitted to point pattern data, using a single fitting function ppm analogous to lm, glm, gam.

The point process model may be any point process that has a conditional intensity which is of `exponential family' form, including spatial trend, dependence on covariates, dependence on marks, and interpoint interactions of arbitrary order.

For example

ppm(data, ~1, Strauss(r=0.1), .....)
will fit the stationary Strauss process with interaction radius 0.1,
ppm(data, ~polynom(x,y,3), Poisson(), ......)
will fit a nonstationary Poisson process whose intensity function is log-cubic in the Cartesian coordinates, and
ppm(data, ~ lo(x,y), Strauss(0.1), .....)
will fit a pairwise interaction process with a Strauss-type interaction and a nonstationary first order term which is a smooth function of the coordinates.

The objects returned by ppm are "fitted point process models". There is a predict method for these objects, which can be used to compute the fitted intensity surface or conditional intensity surface of the process.

Simulations from a fitted model are also possible, using rmh.

Last modified: 30 may 2005