Abstract

Simulated annealing --- moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions --- has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for high-dimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previously-studied tempered transitions, and can be seen as a generalization of a recently-proposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios...

Citations

2801	Optimization by simulated annealing - Kirkpatrick, Gelatt, et al. - 1983
886	Monte Carlo sampling methods using Markov chains and their applications - Hastings - 1970
426	D.: Markov chain Monte Carlo in practice - Gilks, Richardson, et al. - 1996
345	Stochastic Simulation - Ripley - 1987
249	Bayesian Inference in Econometric Models Using Monte Carlo Integration, Econometrica 57 (6 - Geweke - 1989
141	CJ: Markov chain Monte Carlo maximum likelihood - Geyer
132	Annealing markov chain monte carlo with applications to ancestral inference - Geyer, Thompson - 1995
120	Simulated Tempering: a New Monte Carlo Scheme - Marinari, Parisi - 1992
106	Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Stat Sci - Gelman - 1998
73	Regeneration in markov chain samplers - Mykland, Tierney, et al. - 1995
61	Sequential importance sampling for nonparametric Bayes models: The next generation”, Canadian - MacEachern, Clyde, et al. - 1999
55	Sampling from multimodal distributions using tempered transitions - Neal - 1996
5	Chaining via annealing - Evans - 1991