🚀 go-pugleaf

In article <1992Oct4.192217.27919@news2.cis.umn.edu>,
charlie@umnstat.stat.umn.edu (Charles Geyer) writes:
> In article <1992Oct3.210337.21498@news2.cis.umn.edu> I wrote:
> 
>    It makes no sense to compare Gibbs sampling versus simulated annealing, 
>    for example.
> 
> In article <92Oct4.130952edt.243@neuron.ai.toronto.edu>
radford@cs.toronto.edu
> (Radford Neal) replies:
> 
> > Correct, but not for the reasons you perhaps mean. Simulated annealing
> > is a technique that can be used in conjunction with Gibbs sampling 
> > (or other Markov chain methods, such as the Metropolis algorithm) 
> > in order to reach the final equilibrium distribution more quickly.
> 
> Depends on how you think about Markov chain Monte Carlo.  The
> Metropolis-Hastings algorithm produces a Markov chain with a known
> stationary distribution.  This "annealing trick" doesn't.  So far
> from mixing MCMC and simulated annealing, it is not MCMC at all.
> 
> Are there any practically useful convergence results for such schemes
> once Markov chain theory is thrown out the window?
> 

This especially true whenever you want to sample thermodynamic
quantities. Averages must then be well controlled in order
to get significant results.

-----
Frederic Montoya
LSG2M - Ecole des Mines
fmontoya@circe.fr