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Hidden Markov models

Hidden Markov models. Tamkang University Chichang Jou. Questions. Given a short stretch of genomic sequence, how to decide whether it is from a CpG island? Section 3.1 Given a long sequence, how do we find the CpG islands in it? Section 3.2

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Hidden Markov models

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  1. Hidden Markov models Tamkang University Chichang Jou

  2. Questions • Given a short stretch of genomic sequence, how to decide whether it is from a CpG island? • Section 3.1 • Given a long sequence, how do we find the CpG islands in it? • Section 3.2 • Windows of 100 unsatisfactory if CpG islands have sharp boundaries and are of variable lengths

  3. the state sequence is hidden

  4. Questions • Given an HMM and a sequence, what is the most • probable state path • Given an HMM, how likely is a sequence, • what is the overall probability of all the probable • path for this sequence • Given an HMM and a sequence, what is the most • probable state for the i-th position of the sequence • (posterior state probability) • Given an HMM without probability parameters and a • set of sequences, how to estimate the parameters

  5. The value may be very small. Veterbi is normally done in log space

  6. Posterior State Probabilities: by backward algorithms • First calculate the probability of producing the sequence with the i-th symbol • in state k bk(i) fk(i)

  7. Posterior Decoding

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