I am attending a Bioinformatics class and we are learning about HMMs to make inference about DNA sequences.
Well, we recently learned about the forward-backward algorithm that gives us the probability of being in a given state at time t given some sequence of observations. We also learned about the Viterbi algorithm that gives us the most likely sequence of hidden states for a sequence of observations.
I know that taking that most likely state at time t (given by the forward-backward algorithm) won't give us the same result as Viterbi since that sequence may not be valid according to the transition probabilities matrix A.
But I was thinking, if I have a transition probabilities matrix A where all transitions are possible (ie. A(i,j) > 0 for every i,j) may I say that taking the most likely take at each time step (given by the forward-backward algorithm) will give me the same result as Viterbi?
Thanks!
