Hadj-Amar, BeniaminoJewson, JackFiecas, Mark2023-06-272023-06-272023Hadj-Amar B, Jewson J, Fiecas M. Bayesian approximations to hidden semi-Markov models for telemetric monitoring of physical activity. Bayesian Anal. 2023;18(2):547-77. DOI: 10.1214/22-ba13181936-0975http://hdl.handle.net/10230/57372We 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.application/pdfeng© 2023 International Society for Bayesian Analysis. This publication is under a Creative Commons Attribution 4.0 International License.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1214/22-ba1318Markov switching processHamiltonian Monte CarloBayes factortelemetric activity datacircadian rhythminfo:eu-repo/semantics/openAccess