Unformatted text preview: θ = (0 . 24 , . 26 , . 26 , . 24) for { A, C, G, T } . Suppose we know that the sequence S = TCACTATTATCCCTGTTA contains at most one Nanog binding site. Let a be the start position of the site if it exists, and deﬁne a = 0 if S does not contain a site. Only consider the forward strand, i.e., a ∈ { , 1 , ··· , 10 } . Assuming that the prior probability π ( a = i ) is uniform, calculate P ( a = i  S,X,θ ) for i = 0 , 1 , ··· , 10. Hint: P ( a = i  S,X,θ ) ∝ P ( S,a = i  X,θ ) = Z P ( S,a = i  Θ ,θ ) p (Θ  X ) d Θ . 3. Show that the Gibbs sampler is a special case of the MetropolisHastings algorithm. 1...
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This note was uploaded on 11/24/2010 for the course STAT 201a taught by Professor Wu during the Spring '10 term at Pasadena City College.
 Spring '10
 wu
 Probability

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