[R-sig-Geo] Simulating a Gibbs Marked point process

Rolf Turner r.turner at auckland.ac.nz
Wed Apr 10 11:13:59 CEST 2013

On 04/10/2013 02:30 PM, Ferra Xu wrote:
> Hi everybody
> I want to simulate a pattern of points based on maximization of Gibbs marked point process density function by MCMC methods using R. I already know that rmh function in spatstat will do that, but I couldn't find any good example code for that... I don't know how should I determine the objective function that I want to be maximized in each iteration...
I don't really understand what you want to do.  The rmh() [random 
Metropolis Hastings]
function does not proceed by maximizing the density function of the 
(Gibbs) process.  It
uses a Markov chain (whose "states" are point patterns), the 
Metropolis-Hastings algorithm,
and the *conditional intensity* function of the process, to effect the 
simulation.  The transitions
between states are governed by transition probabilities constructed so 
that the *steady
state* distribution of the Markov chain is the distribution of the 
desired process.  There is
no maximization of anything --- at least not in any obvious way, as far 
as I can see.

What do you mean by "I couldn't find any good example code"?  There are 
many examples
of code *using* the rmh() function in the online help.  If you want to 
see the code of rmh()
--- well, R and all of its contributed packages are open source. 
Download the spatstat source
package and have a look! (Be warned --- the heavy lifting is done in C, 
and the code is pretty
subtle and obscure.  By my standards.)


         Rolf Turner

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