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Statistics and Computing

, Volume 25, Issue 2, pp 243–260 | Cite as

On parallel implementation of sequential Monte Carlo methods: the island particle model

  • Christelle VergéEmail author
  • Cyrille Dubarry
  • Pierre Del Moral
  • Eric Moulines
Article

Abstract

The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we study the parallelization of such approximations. The total population of particles is divided into sub-populations, referred to as islands. The particles within each island follow the usual selection/mutation dynamics. We show that the evolution of each island is also driven by a Feynman-Kac semigroup, whose transition and potential can be explicitly related to ones of the original problem. Therefore, the same genetic type approximation of the Feynman-Kac semi-group may be used at the island level; each island might undergo selection/mutation algorithm. We investigate the impact of the population size within each island and the number of islands, and study different type of interactions. We find conditions under which introducing interactions between islands is beneficial. The theoretical results are supported by some Monte Carlo experiments.

Keywords

Particle approximation of Feynman-Kac flow Island models Parallel implementation 

Notes

Acknowledgements

This work is supported by the Agence Nationale de la Recherche through the 2009-2012 project Big MC. The work of Christelle Vergé is financially supported by CNES (Centre National d’Etudes Spatiales) and Onera, The French Aerospace Lab.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Christelle Vergé
    • 4
    • 5
    • 6
    Email author
  • Cyrille Dubarry
    • 2
  • Pierre Del Moral
    • 1
  • Eric Moulines
    • 3
  1. 1.Centre INRIA Bordeaux Sud OuestTalence CedexFrance
  2. 2.SAMOVAR, CNRS UMR 5157Institut Télécom/Télécom SudParisEvryFrance
  3. 3.LTCI, CNRS UMR 8151Institut Télécom/Télécom ParisTechParis Cedex 13France
  4. 4.ONERAThe French Aerospace LabPalaiseauFrance
  5. 5.CNESToulouse Cedex 9France
  6. 6.CMAPEcole PolytechniquePalaiseau CedexFrance

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