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Blocking strategies and stability of particle Gibbs samplers

Published version
Peer-reviewed

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Authors

Singh, SS 
Lindsten, F 
Moulines, E 

Abstract

Sampling from the posterior probability distribution of the latent states of a hidden Markov model is non-trivial even in the context of Markov chain Monte Carlo. To address this Andrieu et al. (2010) proposed a way of using a particle filter to construct a Markov kernel that leaves his posterior distribution invariant. Recent theoretical results establish the uniform ergodicity of this Markov kernel and show that the mixing rate does not deteriorate provided the number of particles grows at least linearly with the number of latent states. However, this gives rise to a cost per application of the kernel that is quadratic in the number of latent states, which can be prohibitive for long observation sequences. Using blocking strategies, we devise samplers that have a stable mixing rate for a cost per iteration that is linear in the number of latent states and which are easily parallelizable.

Description

Keywords

Particle Gibbs sampling, Hidden Markov model, Markov chain Monte Carlo, particle filter

Journal Title

Biometrika

Conference Name

Journal ISSN

0006-3444
1464-3510

Volume Title

104

Publisher

Oxford University Press
Sponsorship
Engineering and Physical Sciences Research Council (EP/K020153/1)
The authors thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme Monte Carlo Inference for Complex Statistical Models when work on this paper was undertaken. This work was supported by the Engineering and Physical Sciences Research Council [grant numbers EP/K020153/1, EP/K032208/1] and the Swedish Research Council [contract number 2016-04278].