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.
- 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.
rmh is generic; it has methods
rmh.ppm (for objects of class
rmh.default (the default).
The actual implementation of the Metropolis-Hastings algorithm is
For details of its use, see
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
# See examples in rmh.default and rmh.ppm