R: Simulated Annealing or Simulated Tempering for Gibbs Point...

rtemper {spatstat.core} | R Documentation

## 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.

### 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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### 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, track=TRUE)

[Package spatstat.core version 2.3-0 Index]