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Unformatted text preview: Hidden Markov Models Chapter 11 CG islands The dinucleotide CG is rare C in a CG often gets methylated and the resulting C then mutates to T Methylation is suppressed in some areas of genome, called CG islands Such CG islands often found around genes Problem: find CG islands in whole genome CG island normal high CG rare CG Two states. Each state emits sequence. Sequence emitted by CG island state is high in CG frequency Concatenation of sequence emissions = genome Biased coin Fair coin more H equal H & T Two states. Each state emits a coin toss result. Sequence emitted by Biased coin state is high in Heads frequency CG Islands and the Fair Bet Casino The CG islands problem can be modeled after a problem named The Fair Bet Casino The game is to flip coins, which results in only two possible outcomes: H ead or T ail. The F air coin will give H eads and T ails with same probability . The B iased coin will give H eads with prob. . The Fair Bet Casino (contd) Thus, we define the probabilities: P(HF) = P(TF) = P(HB) = , P(TB) = The crooked dealer chages between Fair and Biased coins with probability 10% The Fair Bet Casino Problem Input: A sequence x = x 1 x 2 x 3 x n of coin tosses made by two possible coins ( F or B ). Output: A sequence = 1 2 3 n , with each i being either F or B indicating that x i is the result of tossing the Fair or Biased coin respectively. Problem Fair Bet Casino Problem Any observed...
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 Spring '08
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