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.

中文翻译：

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加速度计数据的隐马尔可夫模型混合

通过对跨人群的加速度计数据进行分析，我们引入了隐马尔可夫模型的特定有限混合，这些隐马尔可夫模型具有与此类纵向数据的特定性质相适应的特定特征。我们的模型无需预先指定活动水平，而是通过估算活动的统计数据来表征受试者的身体活动（例如，在不同活动水平上花费的平均时间以及两个活动水平之间转换的可能性）。数据。此外，这种方法可以考虑种群的异质性，并可以定义具有同质体育活动行为的亚群。我们证明，在温和的假设下，该模型暗示对对象进行错误分类的概率随着其测量序列的长度呈指数衰减而降低。模型可识别性也进行了研究。我们还报告了一套全面的数值模拟，以支持我们的理论发现。该方法是受体育锻炼和交通调查的启发而被应用的。