Annealed Importance Sampling

Radford M. Neal, Dept. of Statistics and Dept. of Computer Science, University of Toronto

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 of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers.

Technical Report No. 9805 (revised), Dept. of Statistics (February/September 1998), 25 pages: postscript, pdf.

The above is the revised version of September 1998. The original version of February 1998 is also available: postscript, pdf.

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Associated references: A revised version of this technical report has been published as the following paper:
Neal, R. M. (2001) ``Annealed importance sampling'', Statistics and Computing, vol. 11, pp. 125-139: abstract, associated references.
Annealed importance sampling is related to the method of tempered transitions, described in the following paper:
Neal, R. M. (1996) ``Sampling from multimodal distributions using tempered transitions'', Statistics and Computing, vol. 6, pp. 353-366: abstract, associated references.