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
[If the model is a Poisson process, then Metropolis-Hastings
is not used; the Poisson model is generated directly
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
rmh.default for details.
As of version 1.22-1 of
spatstat a subtle change was
rmh.default(). We had noticed that the results
produced were sometimes not “scalable” in that two models,
differing in effect only by the units in which distances are
measured and starting from the same seed, gave different results.
This was traced to an idiosyncracy of floating point arithmetic.
The code of
rmh.default() has been changed so that the
results produced by
rmh are now scalable. The downside of
this is that code which users previously ran may now give results
which are different from what they formerly were.
In order to recover former behaviour (so that previous results
can be reproduced) set
See the last example in the help for
# See examples in rmh.default and rmh.ppm