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Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers

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Finke, Axel, Johansen, Adam M. and Spanò, Dario (2014) Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers. Annals of the Institute of Statistical Mathematics, Volume 66 (Number 3). pp. 577-609. doi:10.1007/s10463-014-0455-z

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Official URL: http://dx.doi.org/10.1007/s10463-014-0455-z

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Abstract

We develop particle Gibbs samplers for static-parameter estimation in discretely observed piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. A sequential Monte Carlo (SMC) sampler for filtering in PDPs has recently been proposed. We first provide new insight into the consequences of an approximation inherent within that algorithm. We then derive a new representation of the algorithm. It simplifies ensuring that the importance weights exist and also allows the use of variance-reduction techniques known as backward and ancestor sampling. Finally, we propose a novel Gibbs step that improves mixing in particle Gibbs samplers whose SMC algorithms make use of large collections of auxiliary variables, such as many instances of SMC samplers. We provide a comparison between the two particle Gibbs samplers for PDPs developed in this paper. Simulation results indicate that they can outperform reversible-jump MCMC approaches.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title: Annals of the Institute of Statistical Mathematics
Publisher: Springer
ISSN: 0020-3157
Official Date: June 2014
Dates:
DateEvent
June 2014Published
27 March 2014Available
12 March 2013Submitted
Volume: Volume 66
Number: Number 3
Number of Pages: 32
Page Range: pp. 577-609
DOI: 10.1007/s10463-014-0455-z
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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