The Annals of Applied Probability

Importance Sampling for Gibbs Random Fields

Paolo Baldi, Arnoldo Frigessi, and Mauro Piccioni

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Abstract

This existence of an asymptotically efficient importance sampling distribution for estimating small probabilities of statistics of Gibbs random fields is proved, together with its uniqueness, in an appropriate sense. This distribution is also a Gibbs random field associated with an interaction potential that is explicitly given. The particular case of Markov chains is treated. The practical relevance of the results in applications is discussed.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 3 (1993), 914-933.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005372

Digital Object Identifier
doi:10.1214/aoap/1177005372

Mathematical Reviews number (MathSciNet)
MR1233634

Zentralblatt MATH identifier
0780.60047

JSTOR
links.jstor.org

Subjects
Primary: 60G60: Random fields
Secondary: 65C05: Monte Carlo methods 60F10: Large deviations 62G20: Asymptotic properties

Keywords
Large deviations for Gibbs random fields Monte Carlo methods rare events asymptotic efficiency variance reduction techniques

Citation

Baldi, Paolo; Frigessi, Arnoldo; Piccioni, Mauro. Importance Sampling for Gibbs Random Fields. Ann. Appl. Probab. 3 (1993), no. 3, 914--933. doi:10.1214/aoap/1177005372. https://projecteuclid.org/euclid.aoap/1177005372


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