Robust filtering and propagation of uncertainty in hidden Markov models

Allan, Andrew L.

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
• 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
• Related Public URLs: https://arxiv.org/abs/2005.04982