The Annals of Statistics

The pseudo-marginal approach for efficient Monte Carlo computations

Christophe Andrieu and Gareth O. Roberts

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Abstract

We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139–1160], showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method. Theoretical results are given describing the convergence properties of the proposed method, and simple numerical examples are given to illustrate the promising empirical characteristics of the technique. Interesting comparisons with a more obvious, but inexact, Monte Carlo approximation to the marginal algorithm, are also given.

Article information

Source
Ann. Statist. Volume 37, Number 2 (2009), 697-725.

Dates
First available in Project Euclid: 10 March 2009

Permanent link to this document
http://projecteuclid.org/euclid.aos/1236693147

Digital Object Identifier
doi:10.1214/07-AOS574

Mathematical Reviews number (MathSciNet)
MR2502648

Zentralblatt MATH identifier
05561744

Subjects
Primary: 60J22: Computational methods in Markov chains [See also 65C40] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Markov chain Monte Carlo auxiliary variable marginal convergence

Citation

Andrieu, Christophe; Roberts, Gareth O. The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. 37 (2009), no. 2, 697--725. doi:10.1214/07-AOS574. http://projecteuclid.org/euclid.aos/1236693147.


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References

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