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Data augmentation for diffusions
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Papaspiliopoulos, Omiros, Roberts, Gareth O. and Stramer, Osnat (2013) Data augmentation for diffusions. Journal of Computational and Graphical Statistics, Volume 22 (Number 3). pp. 665-688. doi:10.1080/10618600.2013.783484 ISSN 1061-8600.
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Official URL: http://dx.doi.org/10.1080/10618600.2013.783484
Abstract
The problem of formal likelihood-based (either classical or Bayesian) inference for discretely observed multidimensional diffusions is particularly challenging. In principle, this involves data augmentation of the observation data to give representations of the entire diffusion trajectory. Most currently proposed methodology splits broadly into two classes: either through the discretization of idealized approaches for the continuous-time diffusion setup or through the use of standard finite-dimensional methodologies discretization of the diffusion model. The connections between these approaches have not been well studied. This article provides a unified framework that brings together these approaches, demonstrating connections, and in some cases surprising differences. As a result, we provide, for the first time, theoretical justification for the various methods of imputing missing data. The inference problems are particularly challenging for irreducible diffusions, and our framework is correspondingly more complex in that case. Therefore, we treat the reducible and irreducible cases differently within the article. Supplementary materials for the article are available online.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Journal of Computational and Graphical Statistics | ||||||
Publisher: | American Statistical Association | ||||||
ISSN: | 1061-8600 | ||||||
Official Date: | 20 September 2013 | ||||||
Dates: |
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Volume: | Volume 22 | ||||||
Number: | Number 3 | ||||||
Page Range: | pp. 665-688 | ||||||
DOI: | 10.1080/10618600.2013.783484 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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