rmh: Simulate point patterns using the Metropolis-Hastings algorithm.

Description

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

Usage

rmh(model, ...)

Arguments

model

The point process model to be simulated.

...

Further arguments controlling the simulation.

Value

A point pattern, in the form of an object of class "ppp". See rmh.default for details.

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.

Examples

Run this code

# See examples in rmh.default and rmh.ppm