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Robust filtering and propagation of uncertainty in hidden Markov models

Allan, Andrew L.

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Abstract

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and analyze how the induced uncertainty may be propagated through time as we collect new observations, and used to simultaneously provide robust estimates of the hidden signal and to learn the unknown parameters, via techniques based on pathwise filtering and new results on the optimal control of rough differential equations.

Citation

Allan, A. L. (2021). Robust filtering and propagation of uncertainty in hidden Markov models. Electronic Journal of Probability, 26, 1-37. https://doi.org/10.1214/21-ejp633

Journal Article Type Article
Acceptance Date Apr 27, 2021
Online Publication Date May 25, 2021
Publication Date 2021
Deposit Date Jan 24, 2023
Publicly Available Date Jan 24, 2023
Journal Electronic Journal of Probability
Electronic ISSN 1083-6489
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 26
Article Number 73
Pages 1-37
DOI https://doi.org/10.1214/21-ejp633
Public URL https://durham-repository.worktribe.com/output/1182862
Related Public URLs https://arxiv.org/abs/2005.04982

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