Hidden Markov Models on Trees

We present in this chapter hidden Markov models on trees. These models are generalizations of the more traditional one-dimensional hidden Markov models. Traditional hidden Markov models (HMMs) assume hidden states that can take discrete values and are connected through a one-dimensional Markov chain (for a good review on HMMs, see Scott, 2002). In these HMMs, the observations may be discrete or continuous and are conditionally independent given the hidden states. Analogously, hidden Markov models on trees (HMMTs) assume that the values of the latent label process at nodes of a given level are conditionally independent given the latent label process at the immediate coarser level. Moreover, HMMTs assume that the latent label process evolves on a tree in a construction analogous to that described in Chapter 7 for Gaussian processes on trees.