🚀 go-pugleaf

In article <1992Oct5.225003.11916@news2.cis.umn.edu> charlie@umnstat.stat.umn.edu (Charles Geyer) writes:

>[Annealing] doesn't help much.  All it attempts to do is produce one
>realization that is "almost" from the stationary distribution to
>use as the start of the run.
>
>But if the chain mixes very slowly, the average will be near the starting
>point, but not near the expectation one wants to calculate.
>
>On the other hand, if the chain mixes rapidly, the "annealing" isn't
>needed.

Not necessarily. It could be that the chain mixes rapidly once it has
reached the right general region, but that without annealing it takes
a long time to reach that region from whereever it was started.

Anyway, in some problems, notably many in statistical physics,
obtaining a _single_ point form the correct distribution is enough to
solve the problem. An example would be finding the volume of a given
mass of a substance at given temperature and pressure. This quantity
fluctuates, but with a large number of molecules, these fluctuations
are negligible.  A single point from the distribution will almost
certainly give you a good estimate.

    Radford Neal