Hardcore: The Hard Core Point Process Model

In spatstat.model: Parametric Statistical Modelling and Inference for the 'spatstat' Family

The Hard Core Point Process Model

Description

Creates an instance of the hard core point process model which can then be fitted to point pattern data.

Usage

  Hardcore(hc=NA)

Arguments

hc	The hard core distance

Details

A hard core process with hard core distance h and abundance parameter \beta is a pairwise interaction point process in which distinct points are not allowed to come closer than a distance h apart.

The probability density is zero if any pair of points is closer than h units apart, and otherwise equals

f(x_1,\ldots,x_n) = \alpha \beta^{n(x)}

where x_1,\ldots,x_n represent the points of the pattern, n(x) is the number of points in the pattern, and \alpha is the normalising constant.

The function ppm(), which fits point process models to point pattern data, requires an argument of class "interact" describing the interpoint interaction structure of the model to be fitted. The appropriate description of the hard core process pairwise interaction is yielded by the function Hardcore(). See the examples below.

If the hard core distance argument hc is missing or NA, it will be estimated from the data when ppm is called. The estimated value of hc is the minimum nearest neighbour distance multiplied by n/(n+1), where n is the number of data points.

Value

An object of class "interact" describing the interpoint interaction structure of the hard core process with hard core distance hc.

Author(s)

\adrian

and \rolf

References

Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.

Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.

See Also

Strauss, StraussHard, MultiHard, ppm, pairwise.family, ppm.object

Examples

   Hardcore(0.02)
   # prints a sensible description of itself

   ppm(cells ~1, Hardcore(0.05))
   # fit the stationary hard core process to `cells'

   # estimate hard core radius from data
   ppm(cells ~1, Hardcore())
   
     # equivalent:
     ppm(cells ~1, Hardcore)
   

   
     # fit a nonstationary hard core process
     # with log-cubic polynomial trend
     ppm(cells ~ polynom(x,y,3), Hardcore(0.05))
   

spatstat.model documentation built on Sept. 30, 2024, 9:26 a.m.