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
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
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