Forward Algorithm

Finding probability

Section 1 - Page 1
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Finding the probability of an observed sequence

1. Exhaustive search for solution

We want to find the probability of an observed sequence given an HMM - that is, the parameters (P,A,B) are known. Consider the weather example; we have a HMM describing the weather and its relation to the state of the seaweed, and we also have a sequence of seaweed observations. Suppose the observations for 3 consecutive days are (dry,damp,soggy) - on each of these days, the weather may have been sunny, cloudy or rainy. We can picture the observations and the possible hidden states as a trellis.