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

TL;DR

This paper introduces a Bayesian hidden semi-Markov model tailored for analyzing telemetric activity data, enabling flexible, interpretable, and computationally efficient modeling of state durations and incorporating prior knowledge.

Contribution

It presents a novel Bayesian HSMM framework that allows for explicit-duration modeling, Bayesian model selection, and covariate inclusion, with demonstrated application to e-Health data.

Findings

Bayesian approach improves model selection and forecasting.

Efficient inference with negligible statistical error.

First application of Bayesian model selection for state dwell distributions.

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.