Mixture of Hidden Markov Models for the Analysis of Accelerometer data

The work is motivated by the analysis of accelerometer data. 
The aim is to extract summary statistics from such data (e.g., mean time spent at different activity levels and probability of transition between two levels). 
We introduce a finite mixture model of hidden Markov chain for considering heterogeneity of the population.  
This approach avoids to specify by advance the activity levels because it estimates them from the data. 
In addition, it permits to consider the heterogeneity of the population and to deal with the particularities of accelerometer data (many zeros, missing values by sequence...). 
Model identifiability is proved. Moreover, we show that, under mild assumptions, the probability of misclassifying an observation decreases at an exponential rate. Finally, we show how the model can handle missing values. This is a joint work with Marie Du Roy de Chaumary (Crest/ENSAI) and Fabien Navarro (Crest/ENSAI).