The following equation illustrates this idea: conditioned on the previous state s t−1 , the marginal probability of observation y t can be written as: The variable s t−1 = k specifies the mixing weights π k,• for the mixture distribution, while s t indexes the mixture component generating the observation y t .
equation 1says that each row of the transition matrix π specifies a different mixture distribution over the same set of K mixture components φ.