Uncertainty modelling and computational aspects of data association

License
http://creativecommons.org/licenses/by/4.0/

Type
Article

Authors
Houssineau, Jeremie
Zeng, Jiajie
Jasra, Ajay

KAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Preprint Posting Date
2020-09-05

Online Publication Date
2021-08-14

Print Publication Date
2021-09

Date
2021-08-14

Submitted Date
2020-09-08

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.

Citation
Houssineau, J., Zeng, J., & Jasra, A. (2021). Uncertainty modelling and computational aspects of data association. Statistics and Computing, 31(5). doi:10.1007/s11222-021-10039-1

Acknowledgements
This work was supported by Singapore Ministry of Education tier 1 Grant R-155-000-182-114. AJ was additionally supported by KAUST baseline funding.

Publisher
Springer Science and Business Media LLC

Journal
Statistics and Computing

DOI
10.1007/s11222-021-10039-1

arXiv
2009.02517

Additional Links
https://link.springer.com/10.1007/s11222-021-10039-1

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