# Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

arXiv: https://arxiv.org/abs/2006.09061 · HTML: https://mlsanity.com/paper/2006.09061/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Amortized Bayesian Mixture Models](https://mlsanity.com/paper/2501.10229/) (2025)

## Abstract (arXiv)

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.