Multiply all 53 probabilities together and take the

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Unformatted text preview: ample, consider the 26-nucleotide sequence and state path in the middle of Figure 1, where there are 27 transitions and 26 emissions to tote up. Multiply all 53 probabilities together (and take the log, since these are small numbers) and you’ll calculate log P (S,π|HMM,θ) = –41.22. An HMM is a full probabilistic model — the model parameters and the overall sequence ‘scores’ are all probabilities. Therefore, we can use Bayesian probability theory to manipulate these numbers in standard, powerful ways, including optimizing parameters and interpreting the significance of scores. Finding the best state path In an analysis problem, we’re given a sequence, and we want to infer the hidden state path. There are potentially many state paths that could generate the same sequence. We want to find the one with the highest probability. For example, if we were given the HMM and the 26-nucleotide sequence in Figure 1, there are 14 possible paths that have nonzero probability, since the 5′SS must fall on one of 14 internal As or Gs. Figure 1 enumerate...
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