423f11-hmm

423f11-hmm - Hidden Markov Models CMSC 423 Based on Chapter...

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Unformatted text preview: Hidden Markov Models CMSC 423 Based on Chapter 11 of Jones & Pevzner, An Introduction to Bioinformatics Algorithms Eukaryotic Genes & Exon Splicing ATG TAG ATG TAG intron intron intron exon exon exon exon Prokaryotic (bacterial) genes look like this: Eukaryotic genes usually look like this: AUG UAG Exons are concatenated together Introns are thrown away This spliced RNA is what is translated into a protein. mRNA: 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 dont 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 dont 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 dont 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 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 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 can we compute the probability of the entire sequence?...
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This note was uploaded on 01/13/2012 for the course CMSC 423 taught by Professor Staff during the Fall '07 term at Maryland.

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423f11-hmm - Hidden Markov Models CMSC 423 Based on Chapter...

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