R: Simulation of Markov point process model.

sim.mpp {MppMLE}

R Documentation

Simulation of Markov point process model.

Description

A Markov point process model is simulated using a Metropolis-Hastings birth-death algorithm

Usage

sim.mpp(inhompar,interactpar,interactradii,smpsize,space,side=c(1,1,0,0),condint=F,
condext=F,obspoints=matrix(0,0,0),initpoints=matrix(0,0,0),model=1,torus=F,boot=F)

Arguments

`inhompar, interactpar, interactradii`	parameters for Markov point processes, see details on models
`smpsize`	size of MCMC sample
`space`	specifies subsampling of birth-death Markov chain
`side`	specifies simulation window which is [-side[3],side[1]+side[3]] times [-side[4],side[2]+side[4]]
`condint`	if true, conditional simulation with "interior conditioning". Simulation is conditional on the point configuration of obspoints which falls within [0,side[1]] times [0,side[2]]
`condext`	if true, conditional simulation with "exterior conditioning". Simulation is conditional on the point configuration of obspoints which falls outside [0,side[1]] times [0,side[2]]
`obspoints`	point pattern which may be used for conditional simulation (matrix of three columns: x, y and mark)
`initpoints`	initial point pattern for simulations (matrix of three columns: x, y and mark)
`model`	specifies the type of Markov point process being simulated, see details on models
`torus`	if true, toroidal edge correction is used
`boot`	if true, 100 equispaced states (simulated point patterns) from the Markov chain are printed on files boot1.out, boot2.out etc.

Details

This function simulates a Markov point process model using a Metropolis-Hastings birth-death algorithm, see Moeller and Waagepetersen (2003,2006). Interaction parameters are for the exponential family representation. The simulation window is given by [-side[3],side[1]+side[3]] times [-side[4],side[2]+side[4]]. It is possible to condition on points either inside or outside [0,side[1]] times [0,side[2]].

The simulation procedure terminates if the simulated number of points exceeds 5000.

Models

0 is the multiscale process. In this case interactradii[1] specifies the maximal interaction range and interactionradii[2] specifies the number of intervals (of same length) with different interaction parameters. The interaction parameters are given in interactpar. The vector inhompar should have one component: the first order interaction potential (AKA the chemical activity).

1 implements the overlap process used for Norwegian spruces data in Moeller and Waagepetersen (2003). In this case interactradii[0] specifies the factor for computing influence zones.

2 is a multitype (0 or 1) Strauss process where inhompar contains coefficients for a fourth-order polynomial in the y coordinate while interactpar contains 3 interactionparameters for interactions between type 0 points, between type 0 and type 1 points, and between type 1 points. The interaction radius is given in interactradii.

3 is as 2 but only one interactionparameter is used regardless of type of the points.

4 is the hierarchical model used for ants's nests in Moeller and Waagepetersen (2006).

Value

A matrix of dimension of sufficient statistic times smpsize where each column is the sufficient statistic obtained from a point pattern state of the Metropolis-Hastings chain.

Author(s)

Rasmus Waagepetersen rw@math.aau.dk http://www.math.aau.dk/~rw

References

Moeller, J. and Waagepetersen, R. (2003) Statistical inference and simulation of spatial point processes. Chapman & Hall/CRC Press, Boca Raton.

Moeller, J. and Waagepetersen, R. (2006) Modern statistics for spatial point processes. (prepared as a discussion paper for Scandinavian Journal of Statistics).