Open Access
August 2015 On particle Gibbs sampling
Nicolas Chopin, Sumeetpal S. Singh
Bernoulli 21(3): 1855-1883 (August 2015). DOI: 10.3150/14-BEJ629

Abstract

The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the space of the auxiliary variables generated by an interacting particle system. This paper makes the following contributions to the theoretical study of this algorithm. Firstly, we present a coupling construction between two particle Gibbs updates from different starting points and we show that the coupling probability may be made arbitrarily close to one by increasing the number of particles. We obtain as a direct corollary that the particle Gibbs kernel is uniformly ergodic. Secondly, we show how the inclusion of an additional Gibbs sampling step that reselects the ancestors of the particle Gibbs’ extended target distribution, which is a popular approach in practice to improve mixing, does indeed yield a theoretically more efficient algorithm as measured by the asymptotic variance. Thirdly, we extend particle Gibbs to work with lower variance resampling schemes. A detailed numerical study is provided to demonstrate the efficiency of particle Gibbs and the proposed variants.

Citation

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Nicolas Chopin. Sumeetpal S. Singh. "On particle Gibbs sampling." Bernoulli 21 (3) 1855 - 1883, August 2015. https://doi.org/10.3150/14-BEJ629

Information

Received: 1 January 2014; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1333.60164
MathSciNet: MR3352064
Digital Object Identifier: 10.3150/14-BEJ629

Keywords: Feynman–Kac formulae , Gibbs sampling , particle filtering , particle Markov chain Monte Carlo , sequential Monte Carlo

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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