Importance sampling for families of distributions
Madras, Neal ; Piccioni, Mauro
Ann. Appl. Probab., Tome 9 (1999) no. 1, p. 1202-1225 / Harvested from Project Euclid
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This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Motivations for such a study arise in statistics as well as in statistical physics. Two choices of importance sampling distributions are considered in detail: mixtures of the distributions of interest and distributions that are "uniform over energy levels" (motivated by physical applications). We analyze two examples, a "witch's hat" distribution and the mean field Ising model, to illustrate the advantages that such simulation procedures are expected to offer in a greater generality. The connection with the recently proposed simulated tempering method is also examined.
Publié le : 1999-11-14
Classification:  Markov chain Monte Carlo,  importance sampling,  simulated tempering,  Metropolis algorithm,  spectral gap,  Ising model,  60J05,  65C05,  82B80 
@article{1029962870,
     author = {Madras, Neal and Piccioni, Mauro},
     title = {Importance sampling for families of distributions},
     journal = {Ann. Appl. Probab.},
     volume = {9},
     number = {1},
     year = {1999},
     pages = { 1202-1225},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1029962870}
}

Madras, Neal; Piccioni, Mauro. Importance sampling for families of distributions. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp.  1202-1225. http://gdmltest.u-ga.fr/item/1029962870/