R: Saturated Pairwise Interaction Point Process Family

pairsat.family {spatstat.core} | R Documentation

## Saturated Pairwise Interaction Point Process Family

### Description

An object describing the Saturated Pairwise Interaction family of point process models

### Details

Advanced Use Only!

This structure would not normally be touched by the user. It describes the “saturated pairwise interaction” family of point process models.

If you need to create a specific interaction model for use in spatial pattern analysis, use the function `Saturated()` or the two existing implementations of models in this family, `Geyer()` and `SatPiece()`.

Geyer (1999) introduced the “saturation process”, a modification of the Strauss process in which the total contribution to the potential from each point (from its pairwise interaction with all other points) is trimmed to a maximum value c. This model is implemented in the function `Geyer()`.

The present class `pairsat.family` is the extension of this saturation idea to all pairwise interactions. Note that the resulting models are no longer pairwise interaction processes - they have interactions of infinite order.

`pairsat.family` is an object of class `"isf"` containing a function `pairwise$eval` for evaluating the sufficient statistics of any saturated pairwise interaction point process model in which the original pair potentials take an exponential family form.

### Value

Object of class `"isf"`, see `isf.object`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

Geyer, C.J. (1999) Likelihood Inference for Spatial Point Processes. Chapter 3 in O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. Van Lieshout (eds) Stochastic Geometry: Likelihood and Computation, Chapman and Hall / CRC, Monographs on Statistics and Applied Probability, number 80. Pages 79–140.

### See Also

`Geyer` to create the Geyer saturation process.

`SatPiece` to create a saturated process with piecewise constant pair potential.

`Saturated` to create a more general saturation model.

Other families: `inforder.family`, `ord.family`, `pairwise.family`.

[Package spatstat.core version 2.0-0 Index]