Pairwise Markov trees

The Hidden Markov Chain (HMC) models are widely applied in various problems. This success is mainly due to the fact that the hidden model distribution conditional on observations remains a Markov chain distribution, and thus different processings, like Bayesian restorations, are handleable. These models have been recently generalized to "Pairwise" Markov chains, which admit the same processing power and a better modeling one. The aim of this Note is to show that the Hidden Markov trees, which can be seen as extensions of the HMC models, can also be generalized to "Pairwise" Markov trees, which present the same processing advantages and better modelling power.