🚀 go-pugleaf

In article <1992Oct2.095522.9172@vax.oxford.ac.uk> ayoung@vax.oxford.ac.uk
writes:

> Can anyone recommend some good books on the follwing:
>
>[1] importance sampling
>
>[2] Gibbs sampling
>
>[3] Simulated annealing
>
>[4] Genetic algorithms
>
> I'm hoping to find something that (in addition to the maths) also discusses
>and compares the merits of various algorithms for implementing each method.

For a start you could look at Ripley's Stochastic Simulation, which covers
all but the last.

These are not actually all methods for the same problem, so comparing
them is out of the question.

The first two are for simulation or Monte Carlo integration.  The second
pair are random-search optimization methods.  It makes no sense to compare
Gibbs sampling versus simulated annealing, for example.

Even between the first two there is no real "comparison".  The Gibbs sampler
in particular and the Metropolis-Hastings algorithm in general do problems
that are there is no hope of doing by importance sampling.  What is more,
one can combine Metropolis-Hastings and importance sampling (see the discussion
of Geyer and Thompson, JRSS B, 1992) so they aren't really in competition.

Between simulated annealing and genetic algorithms, the answer depends on
who you talk to.  Some people think neither is a very good example of
adaptive random-search optimization.  But I don't think the last word on
the subject has been said by any means.

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu