We recall that a partial probability is calculated as :
t ( j )= Pr(
observation | hidden state is j ) x Pr(all paths to state j at
time t)
We can assume (recursively) that the first term of the product
is available, and now consider the term Pr(all paths to state j
at time t).
To calculate the probability of getting to a state through all
paths, we can calculate the probability of each path to that
state and sum them - for example,
