# rtemper

0th

Percentile

##### Simulated Annealing or Simulated Tempering for Gibbs Point Processes

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

Keywords
spatial, datagen
##### 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.

##### Details

The Metropolis-Hastings simulation algorithm rmh is run for nrep steps at inverse temperature invtemp, then for nrep steps at inverse temperature invtemp, 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.

##### Value

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

rmh.default, rmh.

• rtemper
##### 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)
# }

Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)

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