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The pseudo-marginal approach for efficient Monte Carlo computations

by Christophe Andrieu and Gareth Roberts

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) 11391160], 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.

Key words: Markov chain Monte Carlo; auxiliary variable; marginal; convergence

Full text of the paper (pdf), which has recently appeared in the Annals of Statistics.