  Motivated by the analysis of accelerometer data, we introduce a specific
finite mixture of hidden Markov models with particular characteristics that
adapt well to the specific nature of this type of data. Our model allows for
the computation of statistics that characterize the physical activity of a
subject (\emph{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. Method is motivated by and applied to the PAT
study.
