Given a history of belief states, is there a common method that backtracks the most likely path of ending up in the current belief state?
I have a Markov model which calculates belief states after every step. The belief state is a representation of the most likely states one could be in. A belief state may look like this:
$$b=[1,0,0,0,0],$$ where I am in the state $s_0$ with 100% certainty.
I can store the belief state history like $b_0, b_1, b_2,...b_n$.
Is there a common way to represent and estimate the most likely sates one has been in?
A naive approach could be to just look for the state with the highest value per belief state and take that as the node along the reverse-path. But I am not confident enough, if that is a common and a good practice as it is not considering the fuzziness, which comes with a belief state. But then again, if I would take all states that are bigger than 0, I might not know which state leads to which state and if that transition is even possible.