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The models online are all easy to read except for one thing that confuses me. I do not see how the two matrices interact.

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A Hidden Markov Model is considered 'hidden' because the state variable is unknown at every point. The only known information is the sequence of observations generated by the model, so the sequence of states has to be inferred statistically.

Note: in statistics the concept of hidden variable or latent variable, as opposed to observable variable, is used in various contexts.

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