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Uncertainty modelling and computational aspects of data association
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Houssineau, Jeremie, Zeng, Jiajie and Jasra, Ajay (2021) Uncertainty modelling and computational aspects of data association. Statistics and Computing, 31 . 59. doi:10.1007/s11222-021-10039-1 ISSN 0960-3174.
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Official URL: https://doi.org/10.1007/s11222-021-10039-1
Abstract
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. In order to account for the lack of information about the different aspects of this type of complex system, an alternative representation of uncertainty based on possibility theory is considered. It is shown how analogues of usual concepts such as Markov chains and hidden Markov models (HMMs) can be introduced in this context. In particular, the considered statistical model for multiple dynamical objects can be formulated as a hierarchical model consisting of conditionally independent HMMs. This structure is leveraged to propose an efficient method in the context of Markov chain Monte Carlo (MCMC) by relying on an approximate solution to the corresponding filtering problem, in a similar fashion to particle MCMC. This approach is shown to outperform existing algorithms in a range of scenarios.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Fuzzy sets -- Data processing, Possibility -- Data processing, Monte Carlo method -- Computer programs, Markov processes -- Computer programs | |||||||||
Journal or Publication Title: | Statistics and Computing | |||||||||
Publisher: | Springer | |||||||||
ISSN: | 0960-3174 | |||||||||
Official Date: | 14 August 2021 | |||||||||
Dates: |
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Volume: | 31 | |||||||||
Article Number: | 59 | |||||||||
DOI: | 10.1007/s11222-021-10039-1 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 28 July 2021 | |||||||||
Date of first compliant Open Access: | 27 August 2021 | |||||||||
RIOXX Funder/Project Grant: |
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