Hidden Markov models
A Hidden Markov model, often abbreviated to HMM, which we will use here, is a Bayesian network with a repeating structure that is commonly used to model and predict sequences. In this section, we'll see two applications of this model: one to model DNA gene sequences, and another to model the sequences of letters that make up English text. The basic diagram for an HMM is shown here:
As we can see in the diagram, the sequence flows from left to right and we have a pair of nodes for every entry in the sequence that we are trying to model. Nodes labeled Ci are known as latent states, hidden states, or merely states, as they are typically nodes that are not observable. The nodes labeled Oi are observed states or observations. We will use the terms states and observations.
Now, as this is a Bayesian network, we can immediately identify some key properties. All the observations are independent of each other given their corresponding state. Also, every state is independent of...
