Finding the Best State Sequence I
One method consists of finding the states individually:
For each t, 1? t? T+1, we would like to find Xt that maximizes P(Xt|O, ?).
Let ?i(t) = P(Xt = i |O, ?) = P(Xt = i, O|?)/P(O|?) = (?i(t)?i(t)/?j=1N ?j(t)?j(t))
The individually most likely state is
Xt=argmax1?i?N ?i(t), 1? t? T+1
This quantity maximizes the expected number of states that will be guessed correctly. However, it may yield a quite unlikely state sequence.