## 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.

*Statistics and Computing*, vol. 11, pp. 125-139 (2001).

**Associated references:**
This is the published version of the following technical report:
Neal, R. M. (1998) ``Annealed importance sampling'', Technical Report
No. 9805 (revised), Dept. of Statistics, University of Toronto, 25 pages:
abstract,
associated references,
postscript, pdf.

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.