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Auxiliary likelihood-based approximate Bayesian computation in state space models
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Martin, Gael M., McCabe, Brendan, Frazier, David T., Maneesoonthorn, Worapree and Robert, Christian P. (2019) Auxiliary likelihood-based approximate Bayesian computation in state space models. Journal of Computational and Graphical Statistics, 28 (3). pp. 508-522. doi:10.1080/10618600.2018.1552154 ISSN 1061-8600.
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WRAP-auxiliary-likelihood-based-approximate-Bayesian-computation-state-space-models-Robert-2018.pdf - Accepted Version - Requires a PDF viewer. Download (931Kb) | Preview |
Official URL: https://doi.org/10.1080/10618600.2018.1552154
Abstract
A new approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics computed from observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior; exact inference being feasible only if the statistics are sufficient. With no reduction to sufficiency being possible in the state space setting, we pursue summaries via the maximization of an auxiliary likelihood function. We derive conditions under which this auxiliary likelihood-based approach achieves Bayesian consistency and show that, in the limit, results yielded by the auxiliary maximum likelihood estimator are replicated by the auxiliary score. In multivariate parameter settings a separate treatment of each parameter dimension, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality associated with ABC methods. Three stochastic volatility models for which exact inference is either challenging or infeasible, are used for illustration.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | State-space methods, Bayesian statistical decision theory | ||||||||
Journal or Publication Title: | Journal of Computational and Graphical Statistics | ||||||||
Publisher: | American Statistical Association | ||||||||
ISSN: | 1061-8600 | ||||||||
Official Date: | 2019 | ||||||||
Dates: |
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Volume: | 28 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 508-522 | ||||||||
DOI: | 10.1080/10618600.2018.1552154 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 18 Dec 2018, available online: http://www.tandfonline.com/10.1080/10618600.2018.1552154 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 10 October 2018 | ||||||||
Date of first compliant Open Access: | 18 December 2019 | ||||||||
RIOXX Funder/Project Grant: |
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