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Statistics and Computing

, Volume 17, Issue 3, pp 263–279 | Cite as

On population-based simulation for static inference

  • Ajay Jasra
  • David A. Stephens
  • Christopher C. Holmes
Article

Abstract

In this paper we present a review of population-based simulation for static inference problems. Such methods can be described as generating a collection of random variables {X n } n=1,…,N in parallel in order to simulate from some target density π (or potentially sequence of target densities). Population-based simulation is important as many challenging sampling problems in applied statistics cannot be dealt with successfully by conventional Markov chain Monte Carlo (MCMC) methods. We summarize population-based MCMC (Geyer, Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156–163, 1991; Liang and Wong, J. Am. Stat. Assoc. 96, 653–666, 2001) and sequential Monte Carlo samplers (SMC) (Del Moral, Doucet and Jasra, J. Roy. Stat. Soc. Ser. B 68, 411–436, 2006a), providing a comparison of the approaches. We give numerical examples from Bayesian mixture modelling (Richardson and Green, J. Roy. Stat. Soc. Ser. B 59, 731–792, 1997).

Keywords

Markov chain Monte Carlo Sequential Monte Carlo Bayesian mixture models Adaptive methods 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Ajay Jasra
    • 1
  • David A. Stephens
    • 2
  • Christopher C. Holmes
    • 3
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  3. 3.Department of StatisticsUniversity of OxfordOxfordUK

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