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Lec10-hmm

# Lec10-hmm - Hidden Markov Models CMSC 423 Based on Chapter...

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Hidden Markov Models CMSC 423 Based on Chapter 11 of Jones & Pevzner, An Introduction to Bioinformatics Algorithms

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Checking a Casino Heads/Tails: ↑ ↑ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 ? Suppose either a fair or biased coin was used to generate a sequence of heads & tails. But we don’t know which type of coin was actual used.
Checking a Casino Heads/Tails: ↑ ↑ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 ? Suppose either a fair or biased coin was used to generate a sequence of heads & tails. But we don’t know which type of coin was actual used.

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Checking a Casino Heads/Tails: ↑ ↑ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 ? Suppose either a fair or biased coin was used to generate a sequence of heads & tails. But we don’t know which type of coin was actual used. How could we guess which coin was more likely?
Compute the Probability of the Observed Sequence Pr(x | Fair) = Pr(x | Biased) = X = Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.75 0.75 0.25 0.25 0.25 0.25 0.75

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Compute the Probability of the Observed Sequence Pr(x | Fair) = Pr(x | Biased) = X = Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.75 0.75 0.25 0.25 0.25 0.25 0.75 = 0.5 7 = 0.0078125 = 0.001647949 × × × × × × × × × × × ×
Compute the Probability of the Observed Sequence Pr(x | Fair) = Pr(x | Biased) = X = Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.75 0.75 0.25 0.25 0.25 0.25 0.75 = 0.5 7 = 0.0078125 = 0.001647949 × × × × × × × × × × × × log 2 = Pr(x | Fair) Pr(x | Biased) 0.0078 0.0016 = 2.245 The log-odds score : > 0. Hence “Fair” is a better guess. log 2

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What if the casino switches coins? Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 Probability of switching coins = 0.1 Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.1 0.1
What if the casino switches coins? Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 Probability of switching coins = 0.1 How could we guess which coin was more likely at each position ? Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.1 0.1

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What if the casino switches coins? Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 Probability of switching coins = 0.1 How could we guess which coin was more likely at each position ? How can we compute the probability of the entire sequence? Fair coin: Pr(Heads) = 0.5 Biased coin: Pr(Heads) = 0.75 0.1 0.1
What does this have to do with biology? atg gat ggg agc aga tca gat cag atc agg gac gat aga cga tag tga

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What does this have to do with biology?
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Lec10-hmm - Hidden Markov Models CMSC 423 Based on Chapter...

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