pairsat.family: Saturated Pairwise Interaction Point Process Family
Description
An object describing the Saturated Pairwise Interaction
family of point process modelsDetails
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 one existing implementation of a model in this family,
Geyer().
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.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.