Open Access
June 2023 Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity
Beniamino Hadj-Amar, Jack Jewson, Mark Fiecas
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Bayesian Anal. 18(2): 547-577 (June 2023). DOI: 10.1214/22-BA1318

Abstract

We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows for the development of highly flexible and interpretable models that can integrate available prior information on state durations while keeping a moderate computational cost to perform efficient posterior inference. We show the benefits of choosing a Bayesian approach for HSMM estimation over its frequentist counterpart, in terms of model selection and out-of-sample forecasting, also highlighting the computational feasibility of our inference procedure whilst incurring negligible statistical error. The use of our methodology is illustrated in an application relevant to e-Health, where we investigate rest-activity rhythms using telemetric activity data collected via a wearable sensing device. This analysis considers for the first time Bayesian model selection for the form of the explicit state dwell distribution. We further investigate the inclusion of a circadian covariate into the emission density and estimate this in a data-driven manner.

Acknowledgments

The authors would like to thank the Editor, the Referee, the Associate Editor, David Rossell, and Marina Vannucci for their insightful and valuable comments.

Citation

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Beniamino Hadj-Amar. Jack Jewson. Mark Fiecas. "Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity." Bayesian Anal. 18 (2) 547 - 577, June 2023. https://doi.org/10.1214/22-BA1318

Information

Published: June 2023
First available in Project Euclid: 7 June 2022

MathSciNet: MR4578064
Digital Object Identifier: 10.1214/22-BA1318

Keywords: Bayes factor , circadian rhythm , Hamiltonian Monte Carlo , Markov switching process , telemetric activity data

Vol.18 • No. 2 • June 2023
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