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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
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.
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- Spring '09