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

Pierre del Moral 1 Ajay Jasra 2
1 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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https://hal.inria.fr/hal-01669385
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Submitted on : Wednesday, December 20, 2017 - 7:03:43 PM
Last modification on : Thursday, January 11, 2018 - 6:22:12 AM

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Pierre del Moral, Ajay Jasra. A sharp first order analysis of Feynman–Kac particle models, Part II: Particle Gibbs samplers. Stochastic Processes and their Applications, Elsevier, 2018, 128 (1), pp.354 - 371. ⟨10.1016/j.spa.2017.05.001⟩. ⟨hal-01669385⟩

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