Hidden Markov Models

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Hidden Markov Models

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Markov Chain, Markov Model

• Markov Chain describes a meaningful process that
  can be in any one of a number of states at any
  given time,

Markov Chain Jeff plays guitar.
Markov Model noun verb noun
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Hidden Markov Model

• ...probabilistic model of a group of Markov
  Chains,

Markov Chain(2) Jeff plays flamenco
guitar.
Markov Chain(3) Jeff plays flamenco
guitar poorly.
Hidden Markov Model (noun) (verb) (adjective)
(noun) (adverb)
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Profile Hidden Markov Model

• A Hidden Markov Model built to describe a certain
  set of Markov Chains, that is used to identify
  additional, related chains...

Hidden Markov Model p(Sentence) p(Words in
sentence)(n)(v)(a)(n)(a) x p(Word
order)(n)(v)(a)(n)(a)
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GC Rich vs. Normal
NNNNNNNNNRRRRNNNNNNNNNNNNNNNNNRRRRRRRNNNN
TTACTTGACGCCAGAAATGTATATTTGGTAACCCGACGCTAA
60 AT, 40GC
Are the red regions really GC-rich (R)?
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Training
Based on real data, the relative frequencies
observed for base identification given genomic
location (state probablilties)....
Based on real data, the probability of
entering, or leaving a GC-rich or normal
state N - N (0.9) N - R (0.1) C - C (0.8) C - R
(0.2)
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HMM p(ACGC)
N A 0.3 T 0.3 G 0.2 C 0.2
p(ACGCNRRR)p(NRRR) 0.00123
p(ACGCNNNN)p(NNNN) 0.00175
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HMM p(ACGCC)
N A 0.3 T 0.3 G 0.2 C 0.2
p(ACGCNRRRR)p(NRRRR) 0.0004
p(ACGCCNNNNN)p(NNNNN) 0.000315
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Figure 1
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Figure 2
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Figure 3
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HMM-Others