Singh, SS and Lindsten, F and Moulines, E (2017) *Blocking strategies and stability of particle Gibbs samplers.* Biometrika, 104. pp. 953-969. ISSN 0006-3444

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Particle Gibbs sampling Hidden Markov model Markov chain Monte Carlo particle filter |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 27 Jul 2017 04:06 |

Last Modified: | 11 Jul 2019 02:22 |

DOI: | 10.1093/biomet/asx051 |