An object describing the Saturated Pairwise Interaction family of point process models
Object of class
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
or the two existing implementations of models in this family,
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
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
containing a function
evaluating the sufficient statistics of any saturated pairwise interaction
point process model in which the original pair potentials
take an exponential family form.
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.
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.