--- Additional comments ---- Slide 52 "1. Likelihood: how to calcuate?" I forgot to explain how P(X,path_\ell | \lambda) is calculated at the lecture. Please read carefully the first three lines of mathmatical expressions just under the figure (HMM trellis) to understand the following. (NB: I'm using Latex notation below) Line 1: P(X,path_\ell | \lambda) can be factorised into the product of P(X|path_\ell,\lambda) and P(path_\ell|\lambda). Line 2: The path_\ell, which is shown as the red lines in the figure, denotes the sequence of states: s_0, s_1, s_1, s_1, s_2, s_2, s_3, s_3, s_4 Line 3: The first term on the right hand side of the equation at Line 2 is given as the product of emission probabilities (pdfs to be strict): b_1(x_1) b_2(x_2)....b_3(x_7), and the second term is given as the product of a_{01}... a_{34}.