# rmh

##### Simulate point patterns using the Metropolis-Hastings algorithm.

Generic function for running the Metropolis-Hastings algorithm to produce simulated realisations of a point process model.

- Keywords
- spatial

##### Usage

`rmh(model, ...)`

##### Arguments

- model
- The point process model to be simulated.
- ...
- Further arguments controlling the simulation.

##### Details

The Metropolis-Hastings algorithm can be used to
generate simulated realisations from a wide range of
spatial point processes. For caveats, see below.
The function `rmh`

is generic; it has methods
`rmh.ppm`

(for objects of class `"ppm"`

)
and `rmh.default`

(the default).
The actual implementation of the Metropolis-Hastings algorithm is
contained in `rmh.default`

.
For details of its use, see
`rmh.ppm`

or `rmh.default`

.

[If the model is a Poisson process, then Metropolis-Hastings
is not used; the Poisson model is generated directly
using `rpoispp`

or `rmpoispp`

.]

In brief, the Metropolis-Hastings algorithm is a Markov Chain, whose states are spatial point patterns, and whose limiting distribution is the desired point process. After running the algorithm for a very large number of iterations, we may regard the state of the algorithm as a realisation from the desired point process.

However, there are difficulties in deciding whether the algorithm has run for ``long enough''. The convergence of the algorithm may indeed be extremely slow. No guarantees of convergence are given!

While it is fashionable to decry the Metropolis-Hastings algorithm for its poor convergence and other properties, it has the advantage of being easy to implement for a wide range of models.

##### Value

- A point pattern, in the form of an object of class
`"ppp"`

. See`rmh.default`

for details.

##### See Also

##### Examples

`# See examples in rmh.default and rmh.ppm`

*Documentation reproduced from package spatstat, version 1.7-11, License: GPL version 2 or newer*