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A sharp first order analysis of Feynman–Kac particle models, Part II: Particle Gibbs samplers

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  • Del Moral, Pierre
  • Jasra, Ajay

Abstract

This article provides a new theory for the analysis of the particle Gibbs (PG) sampler (Andrieu et al., 2010). Following the work of Del Moral and Jasra (2017) we provide some analysis of the particle Gibbs sampler, giving first order expansions of the kernel and minorization estimates. In addition, first order propagation of chaos estimates are derived for empirical measures of the dual particle model with a frozen path, also known as the conditional sequential Monte Carlo (SMC) update of the PG sampler. Backward and forward PG samplers are discussed, including a first comparison of the contraction estimates obtained by first order estimates. We illustrate our results with an example of fixed parameter estimation arising in hidden Markov models.

Suggested Citation

  • Del Moral, Pierre & Jasra, Ajay, 2018. "A sharp first order analysis of Feynman–Kac particle models, Part II: Particle Gibbs samplers," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 354-371.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:1:p:354-371
    DOI: 10.1016/j.spa.2017.05.001
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    References listed on IDEAS

    as
    1. 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.
    2. repec:dau:papers:123456789/11498 is not listed on IDEAS
    3. Fredrik Lindsten & Randal Douc & Eric Moulines, 2015. "Uniform Ergodicity of the Particle Gibbs Sampler," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 775-797, September.
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