We denote the partial probability of state j at time t as
t ( j
) - this partial probability is calculated as;
t ( j )=
Pr( observation | hidden state is j ) x Pr(all paths
to state j at time t)
The partial probabilities for the final observation hold the
probability of reaching those states going through all possible
paths - e.g., for the above trellis, the final partial
probabilities are calculated from the paths :
t ( j
) - this partial probability is calculated as;