Forward Algorithm

Finding probability
Definition
Example
Summary
Section 1 - Page 3
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2. Reduction of complexity using recursion

We will consider calculating the probability of observing a sequence recursively given a HMM. We will first define a partial probability, which is the probability of reaching an intermediate state in the trellis. We then show how these partial probabilities are calculated at times t=1 and t=n (> 1).

Suppose throughout that the T-long observed sequence is

Y{k{1}}, Y{k{2}}, .... , Y{k{T}}
2a. Partial probabilities, (a's)
Consider the trellis below showing the states and first-order transitions for the observation sequence dry,damp,soggy;