Blocking strategies and stability of particle Gibbs samplers
Oxford University Press
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Singh, S., Lindsten, F., & Moulines, E. (2017). Blocking strategies and stability of particle Gibbs samplers. Biometrika, 104 (4), 953-969. https://doi.org/10.1093/biomet/asx051
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.
Particle Gibbs sampling, Hidden Markov model, Markov chain Monte Carlo, particle filter
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].
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External DOI: https://doi.org/10.1093/biomet/asx051
This record's URL: https://www.repository.cam.ac.uk/handle/1810/267424