rStraussHard {spatstat.random}

Perfect Simulation of the Strauss-Hardcore Process

Description

Generate a random pattern of points, a simulated realisation of the Strauss-Hardcore process, using a perfect simulation algorithm.

Usage

  rStraussHard(beta, gamma = 1, R = 0, H = 0, W = owin(),
               expand=TRUE, nsim=1, drop=TRUE)

Arguments

beta

intensity parameter (a positive number).

gamma

interaction parameter (a number between 0 and 1, inclusive).

R

interaction radius (a non-negative number).

H

hard core distance (a non-negative number smaller than R).

W

window (object of class "owin") in which to generate the random pattern. Currently this must be a rectangular window.

expand

Logical. If FALSE, simulation is performed in the window W, which must be rectangular. If TRUE (the default), simulation is performed on a larger window, and the result is clipped to the original window W. Alternatively expand can be an object of class "rmhexpand" (see rmhexpand) determining the expansion method.

nsim

Number of simulated realisations to be generated.

drop

Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.

Details

This function generates a realisation of the Strauss-Hardcore point process in the window W using a ‘perfect simulation’ algorithm.

The Strauss-Hardcore process is described in StraussHard.

The simulation algorithm used to generate the point pattern is ‘dominated coupling from the past’ as implemented by Berthelsen and Moller (2002, 2003). This is a ‘perfect simulation’ or ‘exact simulation’ algorithm, so called because the output of the algorithm is guaranteed to have the correct probability distribution exactly (unlike the Metropolis-Hastings algorithm used in rmh, whose output is only approximately correct).

A limitation of the perfect simulation algorithm is that the interaction parameter \gamma must be less than or equal to 1. To simulate a Strauss-hardcore process with \gamma > 1, use rmh.

There is a tiny chance that the algorithm will run out of space before it has terminated. If this occurs, an error message will be generated.

Value

If nsim = 1, a point pattern (object of class "ppp"). If nsim > 1, a list of point patterns.

Author(s)

Kasper Klitgaard Berthelsen and Adrian Baddeley [e-mail]

References

Berthelsen, K.K. and Moller, J. (2002) A primer on perfect simulation for spatial point processes. Bulletin of the Brazilian Mathematical Society 33, 351-367.

Berthelsen, K.K. and Moller, J. (2003) Likelihood and non-parametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling. Scandinavian Journal of Statistics 30, 549-564.

Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.

See Also

rmh, StraussHard.

rHardcore, rStrauss, rDiggleGratton, rDGS, rPenttinen.

Examples

   Z <- rStraussHard(100,0.7,0.05,0.02)
   Y <- rStraussHard(100,0.7,0.05,0.01, nsim=2)