spatstat (version 1.48-0)

rtemper: Simulated Annealing or Simulated Tempering for Gibbs Point Processes

Description

Performs simulated annealing or simulated tempering for a Gibbs point process model using a specified annealing schedule.

Usage

rtemper(model, invtemp, nrep, ..., start = NULL, verbose = FALSE)

Arguments

model

A Gibbs point process model: a fitted Gibbs point process model (object of class "ppm"), or any data acceptable to rmhmodel.

invtemp

A numeric vector of positive numbers. The sequence of values of inverse temperature that will be used.

nrep

An integer vector of the same length as invtemp. The value nrep[i] specifies the number of steps of the Metropolis-Hastings algorithm that will be performed at inverse temperature invtemp[i].

start

Initial starting state for the simulation. Any data acceptable to rmhstart.

...

Additional arguments passed to rmh.default.

verbose

Logical value indicating whether to print progress reports.

Value

A point pattern (object of class "ppp").

Details

The Metropolis-Hastings simulation algorithm rmh is run for nrep[1] steps at inverse temperature invtemp[1], then for nrep[2] steps at inverse temperature invtemp[2], and so on.

Setting the inverse temperature to a value $alpha$ means that the probability density of the Gibbs model, $f(x)$, is replaced by $g(x) = C f(x)^alpha$ where $C$ is a normalising constant depending on $alpha$. Larger values of $alpha$ exaggerate the high and low values of probability density, while smaller values of $alpha$ flatten out the probability density.

For example if the original model is a Strauss process, the modified model is close to a hard core process for large values of inverse temperature, and close to a Poisson process for small values of inverse temperature.

See Also

rmh.default, rmh.

Examples

   stra <- rmhmodel(cif="strauss",
                    par=list(beta=2,gamma=0.2,r=0.7),
                    w=square(10))
   nr <- if(interactive()) 1e5 else 1e4
   Y <- rtemper(stra, c(1, 2, 4, 8), nr * (1:4), verbose=TRUE)