spatstat (version 1.64-1)

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, …, track=FALSE, 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.

track

Logical flag indicating whether to save the transition history of the simulations.

…

Additional arguments passed to rmh.default.

verbose

Logical value indicating whether to print progress reports.

Value

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

If track=TRUE, the result also has an attribute "history" which is a data frame with columns proposaltype, accepted, numerator and denominator, as described in rmh.default.

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 $g(x)=Cf(x{)}^{\alpha }$ 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

# NOT RUN {
   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, track=TRUE)
# }