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Blocking strategies and stability of particle Gibbs samplers
Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
Ecole Polytech, Ctr Math Appl, Route Saclay, F-91128 Palaiseau, France..
2017 (English)In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 104, no 4, p. 953-969Article in journal (Refereed) Published
Abstract [en]

Sampling from the posterior probability distribution of the latent states of a hidden Markov model is nontrivial 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 the posterior distribution invariant. Recent theoretical results have established the uniform ergodicity of this Markov kernel and shown 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.

Place, publisher, year, edition, pages
2017. Vol. 104, no 4, p. 953-969
Keywords [en]
Hidden Markov model, Markov chain Monte Carlo, Particle filter, Particle Gibbs sampling
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-345167DOI: 10.1093/biomet/asx051ISI: 000417325200013OAI: oai:DiVA.org:uu-345167DiVA, id: diva2:1188740
Funder
Swedish Research CouncilAvailable from: 2018-03-08 Created: 2018-03-08 Last updated: 2018-03-08Bibliographically approved

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