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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.

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I found out the issue. I was using the emission probability of current observation whereas I should have used for t+1 th observation. I get correct answer now

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  • $\begingroup$ Congratulations on resolving your issue. You're not the first one to have broken the unity barrier in probability, and with probability $>$ 1, you won't be the last. But unlike some, at least you realized you had probabilities exceeding one. $\endgroup$
    – Mark L. Stone
    Commented May 12, 2016 at 0:26

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