given all observations or given all past observations but sometimes we care about it some a little different so top is filtering middle is smoothing bottom you see in red all the states are marked we want to know what is the most likely joint across all of them now typically adjoins this reason of our many variables not easy to represent so typically what you would do instead of trying to find the fool joint over all of them given all the evidence you'd say let's find the single most likely state combination over all times so what is