Figure 2.

Bayesian graph illustrating the structure of the Hidden Markov model described in the text (Shaded circles indicate variables with known values, unshaded circles indicate hidden variables). Transitions between hidden states x₀ to x_T are governed by the transition matrix A, and are first-order Markovian. Observations o₁ to o_T depend only on the current hidden state and the emission matrix B. Where the parameters of A and B need to be learnt, as depicted here we include appropriate sets of Dirichlet priors, parameterized by the matrices Π^a and Π^b, respectively. Beliefs about the initial hidden state x₀ are governed by the parameter vector d.