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"
. Seermh.default
for details.
See Also
Examples
# See examples in rmh.default and rmh.ppm