Its useful to imagine an hmm generating a sequence

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Unformatted text preview: he linear order in which we expect the states to occur: one or more Es, one 5, one or more Is. So, what’s hidden? It’s useful to imagine an HMM generating a sequence. When we visit a state, we emit a residue from the state’s emission probability distribution. Then, we choose which state to visit next according to the state’s transition probability distribution. The model thus generates two strings of information. One is the underlying state path (the labels), as we transition from state to state. The other is the observed sequence (the DNA), each residue being emitted from one state in the state path. The state path is a Markov chain, meaning that what state we go to next depends only on what state we’re in. Since we’re only given the observed sequence, this underlying state path is hidden—these are the residue labels that we’d like to infer. The state path is a hidden Markov chain. The probability P (S,π|HMM,θ) that an HMM with parameters θ generates a state path π and an observed sequence S is the product of all the emission probabilities and transition probabilities that were used. For ex...
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