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2021 Robust filtering and propagation of uncertainty in hidden Markov models
Andrew L. Allan
Author Affiliations +
Electron. J. Probab. 26: 1-37 (2021). DOI: 10.1214/21-EJP633


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.

Funding Statement

The author gratefully acknowledges financial support by the Swiss National Science Foundation via Project 200021_184647.


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Andrew L. Allan. "Robust filtering and propagation of uncertainty in hidden Markov models." Electron. J. Probab. 26 1 - 37, 2021.


Received: 11 May 2020; Accepted: 27 April 2021; Published: 2021
First available in Project Euclid: 25 May 2021

arXiv: 2005.04982
Digital Object Identifier: 10.1214/21-EJP633

Primary: 60G35 , 60L50 , 60L90

Keywords: Filtering , Hidden Markov model , parameter uncertainty , pathwise optimal control , Rough paths


Vol.26 • 2021
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