## Annealed importance sampling (2001)

Venue: | In Statistics and Computing |

Citations: | 165 - 3 self |

### BibTeX

@INPROCEEDINGS{Neal01annealedimportance,

author = {Radford M. Neal},

title = {Annealed importance sampling},

booktitle = {In Statistics and Computing},

year = {2001},

pages = {125--139}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 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. 1

### Citations

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Citation Context ... An alternative is to obtain a sample of dependent points by simulating a Markov chain that converges to the distribution of interest, as in the Metropolis-Hastings algorithm (Metropolis, et al 1953; =-=Hastings 1970-=-). Such Markov chain methods have long been used in statistical physics, and are now widely applied to statistical problems, as illustrated by the papers in the book edited by Gilks, Richardson, and S... |

653 | Bayesian learning for neural networks
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(Show Context)
Citation Context ...hat these vary smoothly. Demonstrations on simple distributions in Section 5 and on a statistical problem in Section 6 confirm this. 3Annealed importance sampling is related to tempered transitions (=-=Neal 1996-=-), which are another way of modifying the annealing procedure so as to produce correct results. As discussed in Section 7, annealed importance sampling will sometimes be preferable to using tempered t... |

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(Show Context)
Citation Context ...nspired by the idea of “annealing” as a way of coping with isolated modes, but it may be attractive 1even when multimodality is not a problem. Importance sampling works as follows (see, for example, =-=Geweke 1989-=-). Suppose that we are interested in a distribution for some quantity, x, with probabilities or probability densities that are proportional to the function f(x). Suppose also that computing f(x) for a... |

218 |
Markov chain Monte Carlo maximum likelihood
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(Show Context)
Citation Context ...er to produce asymptotically correct estimates have been developed in the past, including simulated tempering (Marinari and Parisi 1992; Geyer and Thompson 1995) and Metropolis coupled Markov chains (=-=Geyer 1991-=-). The method of tempered transitions (Neal 1996) is closely related to the annealed importance method of this paper. The tempered transition method samples from a distribution of interest, p0, using ... |

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Annealing Markov chain Monte Carlo with applications to ancestral inference
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(Show Context)
Citation Context ...eral ways of modifying the simulated annealing procedure in order to produce asymptotically correct estimates have been developed in the past, including simulated tempering (Marinari and Parisi 1992; =-=Geyer and Thompson 1995-=-) and Metropolis coupled Markov chains (Geyer 1991). The method of tempered transitions (Neal 1996) is closely related to the annealed importance method of this paper. The tempered transition method s... |

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(Show Context)
Citation Context ...o tempered transitions Several ways of modifying the simulated annealing procedure in order to produce asymptotically correct estimates have been developed in the past, including simulated tempering (=-=Marinari and Parisi 1992-=-; Geyer and Thompson 1995) and Metropolis coupled Markov chains (Geyer 1991). The method of tempered transitions (Neal 1996) is closely related to the annealed importance method of this paper. The tem... |

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(Show Context)
Citation Context ...arkov chains). Ratios of normalizing constants can also be obtained when using annealed importance sampling itself, which from this perspective can be seen as a form of thermodynamic integration (see =-=Gelman and Meng 1998-=-). One might expect a thermodynamic integration estimate based on a finite number of points to suffer from systematic error, but the results of this paper show that the annealed importance sampling es... |

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(Show Context)
Citation Context ...r of interpolating distributions, provided that these vary smoothly. Demonstrations on simple distributions in Section 5 confirm this. Annealed importance sampling is related to tempered transitions (=-=Neal 1996-=-), which are another way of modifying the annealing procedure so as to produce correct results. As discussed in Section 6, annealed importance sampling will sometimes be preferable to using tempered t... |

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