An HMM is a specific case of state space model in which the latent variables are discrete and multinomial variables. From the graphical representation, we can also consider an HMM to be a double stochastic process consisting of a hidden stochastic Markov process (of latent variables) that we cannot observe directly, and another stochastic process that produces a sequence of the observation given the first process.
Before moving on to the parameterization, let's consider an example of coin-tossing to get an idea of how it works. Assume that we have two unfair coins, M1 and M2, with M1 having a higher probability (70%) of getting heads and M2 having a higher probability (80%) of getting tails. Someone sequentially flips these two coins, however, we do not know which one. We can only observe the outcome, which can either be heads (H) or tails (T):
We can consider the...
