simulateRFHC: Simulate Finite Gibbs Hardcore Model with Smoothly Varying...

In antiphon/rfhc: Random field + Hardcore Gibbs model

Description

Simulate stationary and isotropic 2D Mat\'ern Gaussian random field using Markov approximation in a grid.

Then make exponential transformation, and get a field (say) R.

Then simulate finite Gibbs hardcore model so that the repulsion radius at s is R(s).

Usage

simulateRFHC(n=100, iter=1e5, ncol=50, window=square(),	
             r.field.pars=c(mean=-2, tau=5, range=0.4, nu=2), 
             start.pattern=NULL, pre.r.field=NULL, giveup=1e6, 
             type="HC", dbg=0, seed, cyclic, expand)

Arguments

n	Target number of points to generate into the simulated pattern.
iter	Number of Metropolis-Hastings iterations.
ncol	Grid x-dimension. y-dimension is computed using window so that aspect ratio is 1.
window	Simulation window, in spatstat's owin-object format.
pre.r.field	Pre-computed R-field. In spatstat's im-format. If null we simulate it with given parameters using the function simulateGMRF.
giveup	See “Details”.
type	Type of repulsion. HC is hard-core, HS hard-spheres (not yet supported).
seed	Random seed. If not given a system time based random seed is used.
start.pattern	Starting pattern. If null we start with a single uniformly random point.
dbg	Verbose output during simulation.
r.field.pars, cyclic	Parameters for the field simulation, see simulateGMRF and “Details”.

Details

The function simulates a finite Gibbs hard-core model where the hard-core radius, say R, depends on the spatial location and varies smoothly in the window. We use an exponentially transformed Mat\'ern family Gaussian random field for the smooth variation.

The (non-negative) R-field can be provided using parameter pre.r.field. It should be produced with the function simulateGMRF. If a field is not provided, the members of vector r.field.pars are used to simulate the field: we first simulate GMRF using simulateGMRF to get (say) Y, and then transform this to R=exp(Y+mean), where ‘mean’ is given in r.field.pars.

Given the R-field, we simulate a finite Gibbs hard-core model where the hard-core radius at s is given by R(s) (with nearest grid point approximation). We start with an empty configuration x. Until x has n points in it, we

i1. Suggest a uniform random point x1 from the window.
i2. If the union (x,x1) does not violate hardcore rule, accept the union as the new pattern. If violates (i.e. exists j s.t. ||x1-xj||<min(R(x1), R(xj)) ), discard x1.
i3. If 1000 consecutive discards, remove a randomly chosen point from x.
i4. Goto i1.

This loop is run until EITHER x has n points in it OR giveup amount of iterations has been run.

After the initial configuration is set, we move a single point, i.e. change location uniformly, and accept the move if hard-core rule is not violated. This is repeated iter times.

The first step (i1-i4) is a birth-and-death process simulation, and the second step is Metropolis-Hastings simulation, see reference.

Value

Object of class rfhcSim which is the same as object of class ppp with the additional elements

$parameters : the parameters provided
$r.field : The R-field used in simulation.

References

Rajala, T. and Penttinen, A. (2012): Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range, Comp. Stat. Data An.

Moller, Waagepetersen (2004) Statistical Inference and Simulation for Spatial Point Processes Chapman&Hall/CRC

See Also

plot.rfhcSim-method for plotting the field and the pattern simultaneously.

Examples

 y <- simulateRFHC()
 plot(y)

antiphon/rfhc documentation built on May 10, 2019, 12:20 p.m.