Re: [Gretl-users] MCMC for dummies?
On Sat, 25 Aug 2012, Allin Cottrell wrote:
This may appear to be totally off-topic but it's not entirely
so,
given that we've had a "feature request" at sourceforge for a Gibbs
sampler implementation. Anyway, does anyone have a recommendation
for a sort of "Markov Chain Monte Carlo for dummies" -- a useful
book, article or website?
I'm no specialist on this, so I may be not entirely correct, but basically
MCMC is a family of methods for drawing pseudo-random numbers from given
(conditional) distributions. A good starting point is
Chib and Greenberg(1995), "Understanding the Metropolis-Hastings
Algorithm", The American Statistician, Vol. 49(4), pp. 327-335
or its predecessor,
Casella and George(1992), "Explaining the Gibbs sampler", The American
Statistician, Vol. 46(3), pp. 167-174.
Once you've got a steady supply of pseudo-random draws, you may use them
to simulate several useful object. Bayesians, for example, use them a lot
to explore the posterior distribution of a parameter. In a frequentist
context, you may use those draws to compute a simulated log-likelihood and
then maximise it. See eg
Gourieroux and Monfort(1996), Simulation-based econometric methods, Oxford
UP
This said, I think Lee is much more knowledgeable than me on this.
Over to you, Prof. Adkins :)
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Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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