# rtemper

##### 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.

##### 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.

##### 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.

##### 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`

.

##### See Also

##### 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)
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*