an initial probability distribution over states. π i is the probability that the Markov chain will start in state i. Some states j may have π j = 0, meaning that they cannot be initial states. Also, n i=1 π i = 1 A first-order hidden Markov model instantiates two simplifying assumptions. First, as with a first-order Markov chain, the probability of a particular state depends only on the previous state: