| rmh {spatstat} | R Documentation |
Generic function for running the Metropolis-Hastings algorithm to produce simulated realisations of a point process model.
rmh(model, ...)
model |
The point process model to be simulated. |
... |
Further arguments controlling the simulation. |
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.
A point pattern, in the form of an object of class "ppp".
See rmh.default for details.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
# See examples in rmh.default and rmh.ppm