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November 1999 Importance sampling for families of distributions
Neal Madras, Mauro Piccioni
Ann. Appl. Probab. 9(4): 1202-1225 (November 1999). DOI: 10.1214/aoap/1029962870


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.


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Neal Madras. Mauro Piccioni. "Importance sampling for families of distributions." Ann. Appl. Probab. 9 (4) 1202 - 1225, November 1999.


Published: November 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0966.60061
MathSciNet: MR1728560
Digital Object Identifier: 10.1214/aoap/1029962870

Primary: 60J05
Secondary: 65C05 , 82B80

Keywords: importance sampling , Ising model , Markov chain Monte Carlo , Metropolis algorithm , simulated tempering , spectral gap

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 4 • November 1999
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