Creates an instance of an Ord-type interaction point process model which can then be fitted to point pattern data.
Ord(pot, name)An S language function giving the user-supplied interaction potential.
Character string.
An object of class "interact"
describing the interpoint interaction
structure of a point process.
Ord's point process model (Ord, 1977) is a Gibbs point process of infinite order. Each point \(x_i\) in the point pattern \(x\) contributes a factor \(g(a_i)\) where \(a_i = a(x_i, x)\) is the area of the tile associated with \(x_i\) in the Dirichlet tessellation of \(x\).
Ord (1977) proposed fitting this model to forestry data
when \(g(a)\) has a simple ``threshold'' form. That model is
implemented in our function OrdThresh.
The present function Ord implements the case of a
completely general Ord potential \(g(a)\)
specified as an S language function pot.
This is experimental.
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283--322.
Ord, J.K. (1977) Contribution to the discussion of Ripley (1977).
Ord, J.K. (1978) How many trees in a forest? Mathematical Scientist 3, 23--33.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 -- 212.