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Smoothing With Couplings of Conditional Particle Filters
Harvard Univ, MA 02138 USA.
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
Uppsala Univ, Sweden.
2019 (English)In: Journal of the American Statistical Association, ISSN 0162-1459, E-ISSN 1537-274XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

In state-space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and CI can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly informative observations, and for a realistic Lotka-Volterra model with an intractable transition density. Supplementary materials for this article are available online.

Place, publisher, year, edition, pages
AMER STATISTICAL ASSOC , 2019.
Keywords [en]
Couplings; Debiasing techniques; Parallel computation; Particle filtering; Particle smoothing
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-158584DOI: 10.1080/01621459.2018.1548856ISI: 000470537800001OAI: oai:DiVA.org:liu-158584DiVA, id: diva2:1334801
Note

Funding Agencies|Swedish Foundation for Strategic Research (SSF) via the project Probabilistic Modeling and Inference for Machine Learning [ICA16-0015]; Swedish Foundation for Strategic Research (SSF) via the project ASSEMBLE [RIT15-0012]; Swedish Research Council (VR) via the project Learning of Large-Scale Probabilistic Dynamical Models [2016-04278]; Swedish Research Council (VR) via the project NewLEADS-New Directions in Learning Dynamical Systems [621-2016-06079]; National Science Foundation [DMS-1712872]

Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-08-09

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf