2. Given nucleotide counts { to model a DNA sequence V, where Q den...

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2. Given nucleotide counts { to model a DNA sequence V, where Q denotes the DNA alphabet with an independent model. Assume that the prior density of nucleotide probabilities p = { px : XES} is given by a Dirichlet distribution with parameters = X XEQ a) Derive the likelihood f(y/p), the prior f (p) and the joint density f(y,p) of the sequence. b) Show that the marginal density f (y) is given by 1 nx + B X f(y) = n + B ) XEQ nx n n n! where n = nx and the binomial coefficient XEQ (n-r)la! - c) Find the posterior density f(ply). d) Derive the maximum a posteriori (MAP) estimates of model parameters.

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