7th February 2005 — Annealing Review
If you are unfamiliar with normal MCMC methods, such as the Metropolis algorithm, read up on that instead as it will not be reviewed. Try either the review above or David’s book.
For reference the papers Iain used were:
- Simulated Anealing:
- Cluster Replica / Metropolis coupled Markov chains:
- Low-temperature properties of the +/-J Ising spin glass in two dimensions. Jian-Sheng Wang and Robert H. Swendsen. Phys Review B 38(7) 1988. url
- …should have looked at others.
- Expanded ensembles / Simulated tempering:
- Tempered transitions. AIC:
- Multicanoncial Ensemble (or umbrella sampling):
Particularly recommended is “Tempered transitions” for its discussion.
“Regeneration” has been applied to simulated tempering and multicanonical ensemble methods. Perhaps allows “pre-simulation” for weights to be a bit less wasteful. I’m afraid you’ll have to chase the references yourself. Naively it is probably fairly easy to apply.
Also recommended is the following review paper shown to him afterwards:
- Extended Ensemble Monte Carlo. Y Iba. Int J Mod Phys C [Computational Physics and Physical Computation] 12(5):623-656. 2001. arxiv, journal.
And this oft-cited paper:
- Simulating normalizing constants: from importance sampling to bridge sampling to path sampling, Andrew Gelman and Xiao-Li Meng, Statist. Sci. 13 (1998), no. 2, 163-185.
Note that we did not cover the neat methods in BayeSys or Nested Sampling, acceptance ratio methods (as such), Hamiltonian Monte Carlo (as found in fbm), Dragging fast variables, a bunch of classical techniques, some newer variations of the above methods, or probably a zillion other annealing-related ideas.