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Particle Markov chain Monte Carlo methods

Author

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  • Christophe Andrieu
  • Arnaud Doucet
  • Roman Holenstein

Abstract

Summary. Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non‐linear state space model and a Lévy‐driven stochastic volatility model.

Suggested Citation

  • Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
  • Handle: RePEc:bla:jorssb:v:72:y:2010:i:3:p:269-342
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    File URL: https://doi.org/10.1111/j.1467-9868.2009.00736.x
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    References listed on IDEAS

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