The pseudo-marginal approach for efficient Monte Carlo computations

2009/03/10 by Christophe Andrieu, Gareth O. Roberts · 719 citations
Computer Science · Mathematics · #Algorithm #Algorithms and Data Compression #Applied mathematics #Bayesian Methods and Mixture Models #Computation #Convergence (economics) #Hybrid Monte Carlo #Marginal distribution #Marginal likelihood #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Maximum likelihood #Monte Carlo method #Random variable #Simple (philosophy) #Statistics #math.ST #msc:60J22 #msc:60K35 #stat.TH

paper · pdf · doi:10.1214/07-aos574

published in The Annals of Statistics 37(2) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/07-AOS574 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2009/03/10 · arxiv created 2009/03/31 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06

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.

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Related

• Pseudo-Marginal Hamiltonian Monte Carlo
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