Ord: Generic Ord Interaction model

Description

Creates an instance of an Ord-type interaction point process model which can then be fitted to point pattern data.

Usage

Ord(pot, name)

Arguments

pot

An S language function giving the user-supplied interaction potential.

name

Character string.

Value

An object of class "interact" describing the interpoint interaction structure of a point process.

Details

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.

References

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.