I am trying to understand the Baum Welch algorithm by implementing it in xls. I have chosen a simple example of observations from a loaded (L) vs fair (F) die. I calculate the forward and backward probabilities for L and F states. I then calculate the probability of observations. I know the calculations till this point are correct, since i get the same p(observations) for each row of data.
i.e.p(observations)= forward probability(L)*forward probability(F)+ backward probability(L) * backward probability(F) is same for all rows as it should be
Then I proceed to calculate the transition probabilities. Here I find that the value of the transition probability for the state transition L->L is coming to be above 1.For other states the values seem to be correct
I calculate the transition probabilities for L->L for each row as follows: T(L->L)
(Forward_probability(L,t)* Transition(L->L)* emission(observation|L) * backward_probability(L,t+1))/ probability(observations)
The estimated probability = sum( T(L->L) )/sum(L|observation ) I am unable to find why my transition probability has value > 1.
Any help will be appreciated.