Annals of Applied Probability

Importance sampling for families of distributions

Neal Madras and Mauro Piccioni

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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.

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Ann. Appl. Probab., Volume 9, Number 4 (1999), 1202-1225.

First available in Project Euclid: 21 August 2002

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 65C05: Monte Carlo methods 82B80: Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]

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


Madras, Neal; Piccioni, Mauro. Importance sampling for families of distributions. Ann. Appl. Probab. 9 (1999), no. 4, 1202--1225. doi:10.1214/aoap/1029962870.

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