Is the forward probability matrix created with respect to the sequence or ONLY the hidden markov model? My understanding is that the forward procedure doesn’t care about the true sequence at hand. Its function (as far as i understand) is to simply take into account the current Markov model and for every hidden state calculate the probability of finding each and every observation, this would explain why it is possible to get a result that doesn’t align with the true sequence.
Can someone correct me if i am wrong? Am i correct or incorrect?