Multichain Hidden Markov and semi-Markov Models: formalization, inference and applications.

Résumé :

Hidden Markov Models and Hidden Semi-Markov Models are very popular statistical models for the study of dynamical process which cannot be observed directly. In several applications, in particular when space is involved, the hidden chain and the observed times series are actually multidimensional with structured dependencies between the variables at time t and the variables at time t+1. In this talk we define the framework of multichain HMM that enables to present in an unified way existing models from literature and also generalise them. We illustrate how such models can be usefull to model dynamics in ecology. We then discuss inference of multichain HMM in the context of the EM algorithm. We explain why for some structure of multichain HMM exact inference will remain tractable, while for others it is out of reach. Finally we consider the extension to the semi-Markov case and we propose the first rigorous definition of a multichain HSMM.