spatstat.core: rPenttinen – R documentation

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rPenttinen

Perfect Simulation of the Penttinen Process

Description

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

Usage

rPenttinen(beta, gamma=1, R, W = owin(), expand=TRUE, nsim=1, drop=TRUE)

Arguments

`beta`	intensity parameter (a positive number).
`gamma`	Interaction strength parameter (a number between 0 and 1).
`R`	disc radius (a non-negative number).
`W`	window (object of class `"owin"`) in which to generate the random pattern.
`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 Penttinen point process in the window W using a ‘perfect simulation’ algorithm.

Penttinen (1984, Example 2.1, page 18), citing Cormack (1979), described the pairwise interaction point process with interaction factor

h(d) = exp(theta * A(d)) = gamma^(A(d))

between each pair of points separated by a distance $d$. Here A(d) is the area of intersection between two discs of radius R separated by a distance d, normalised so that A(0) = 1.

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).

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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, based on original code for the Strauss process by Kasper Klitgaard Berthelsen.

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.

Cormack, R.M. (1979) Spatial aspects of competition between individuals. Pages 151–212 in Spatial and Temporal Analysis in Ecology, eds. R.M. Cormack and J.K. Ord, International Co-operative Publishing House, Fairland, MD, USA.

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

Penttinen, A. (1984) Modelling Interaction in Spatial Point Patterns: Parameter Estimation by the Maximum Likelihood Method. Jyvaskyla Studies in Computer Science, Economics and Statistics 7, University of Jyvaskyla, Finland.

Examples

X <- rPenttinen(50, 0.5, 0.02)
   Z <- rPenttinen(50, 0.5, 0.01, nsim=2)

spatstat.core

Core Functionality of the 'spatstat' Family

v2.1-2

GPL (>= 2)

Authors

Adrian Baddeley [aut, cre], Rolf Turner [aut], Ege Rubak [aut], Kasper Klitgaard Berthelsen [ctb], Achmad Choiruddin [ctb], Jean-Francois Coeurjolly [ctb], Ottmar Cronie [ctb], Tilman Davies [ctb], Julian Gilbey [ctb], Yongtao Guan [ctb], Ute Hahn [ctb], Kassel Hingee [ctb], Abdollah Jalilian [ctb], Marie-Colette van Lieshout [ctb], Greg McSwiggan [ctb], Tuomas Rajala [ctb], Suman Rakshit [ctb], Dominic Schuhmacher [ctb], Rasmus Plenge Waagepetersen [ctb], Hangsheng Wang [ctb]

Initial release

2021-04-17