Open Access
December 2020 Mixture of hidden Markov models for accelerometer data
Marie Du Roy de Chaumaray, Matthieu Marbac, Fabien Navarro
Ann. Appl. Stat. 14(4): 1834-1855 (December 2020). DOI: 10.1214/20-AOAS1375


Motivated by the analysis of accelerometer data taken across a population of individuals, we introduce a specific finite mixture of hidden Markov models with particular characteristics that adapt well to the specific nature of this type of longitudinal data. Our model allows for the computation of statistics that characterize the physical activity of a subject (e.g., the mean time spent at different activity levels and the probability of the transition between two activity levels) without specifying the activity levels in advance but by estimating them from the data. In addition, this approach allows the heterogeneity of the population to be taken into account and subpopulations with homogeneous physical activity behavior to be defined. We prove that, under mild assumptions, this model implies that the probability of misclassifying a subject decreases at an exponential decay with the length of its measurement sequence. Model identifiability is also investigated. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The method is motivated by and applied to the Physical Activity and Transit Survey.


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Marie Du Roy de Chaumaray. Matthieu Marbac. Fabien Navarro. "Mixture of hidden Markov models for accelerometer data." Ann. Appl. Stat. 14 (4) 1834 - 1855, December 2020.


Received: 1 March 2020; Revised: 1 July 2020; Published: December 2020
First available in Project Euclid: 19 December 2020

MathSciNet: MR4194250
Digital Object Identifier: 10.1214/20-AOAS1375

Keywords: Accelerometer data , Hidden Markov model , longitudinal data , missing data , Mixture models

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.14 • No. 4 • December 2020
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