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mcmc

• To: mathgroup at smc.vnet.net
• Subject: [mg53040] mcmc
• From: astymc2000 at yahoo.fr (astymc)
• Date: Tue, 21 Dec 2004 05:19:17 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

jose.m.ramon at uv.es (jose) writes:

>Hi!
>I'd like to know if there is something made for Mathematica using
>Montecarlo  Markov Chain numerical integration methods. I'd be very
>appreciate if somebody tells me how to find it. Thanks in advance.
>Best regards,
>Jose M. <jose.m.ramon at uv.es>

MCMC methods such as metropolis-hastings and gibbs sampling can be
programmed directly in Mathematica. The algorithms are available in
many books or articles on the subject.  Lots of algorithms have been
written in S-plus or Xlispstat, but can be modified for Mathematica
code.

Code can been found on the web.  I found a MH algorithem (in S-plus),
and  have been modifying it to suite each problem as they come up.  I
can  provide the address later if you're interested.  

There are programs specifically for MCMC.  One is BUGS, which is
available on the web. A search can easily bring up the address. 
(search BUGS, Bayesian).  

I do know of one paper called "Bayesian Statistics Using Mathematica"
in
the American Statistician, 1995 vol. 49.  Authors Cook and Broemeling.

It might be of interest to you in exploring your specific problem.  It
discusses Monte Carlo integration and sampling-importance-resampling.
(but not MCMC exactly)

Laura