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.
Publié le : 1993-08-14
Classification:
Large deviations for Gibbs random fields,
Monte Carlo methods,
rare events,
asymptotic efficiency,
variance reduction techniques,
60G60,
65C05,
60F10,
62G20
@article{1177005372,
author = {Baldi, Paolo and Frigessi, Arnoldo and Piccioni, Mauro},
title = {Importance Sampling for Gibbs Random Fields},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 914-933},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005372}
}
Baldi, Paolo; Frigessi, Arnoldo; Piccioni, Mauro. Importance Sampling for Gibbs Random Fields. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 914-933. http://gdmltest.u-ga.fr/item/1177005372/