One drawback of the Gibbs sampler, and many other types of
Metropolis-Hastings samplers, is that the chain may take a long time
to sample the whole state space because of the strong dependence
between each realization of the chain. If the distribution 
is
multimodal, the sampler may remain near a local mode very long because
it has to step through low probability regions to reach the other
modes. One solution is to make the distribution more uniform by
raising its ``temperature''. The temperature 
is a parameter
indexing a sequence of distributions in the following way:
We can see that the distribution becomes uniform when 
. For a Metropolis sampler, the acceptance
probabilities with a ``heated'' distribution become
The chain is started with a high temperature distribution. The
distribution is progressively cooled down to the distribution of
interest 
obtained when 
. The procedure helps the
sampler to cover the entire sample space of the distribution
. For an application of simulated annealing in a genetic context,
see Lin et al [5].