MIXTURE OF HIDDEN MARKOV MODELS FOR ACCELEROMETER DATA

• 成果类型: Article
• 署名作者: de Chaumaray, Marie Du Roy; Marbac, Matthieu; Navarro, Fabien
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/20-AOAS1375
• 发表日期: 2020
• 页码: 1834-1855
• 关键词: sleep-wake identification; physical-activity; maximum-likelihood; longitudinal data; Identifiability; extension; profiles; duration; identify; disease

摘要

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.