HMM You are employed by a biomedical lab to create a system which automatically reads an RNA triplet fed to it. For each

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Hmm You Are Employed By A Biomedical Lab To Create A System Which Automatically Reads An Rna Triplet Fed To It For Each 1 (80.45 KiB) Viewed 85 times

HMM You are employed by a biomedical lab to create a system which automatically reads an RNA triplet fed to it. For each location of the RNA triplet, you can assume there only two (2) possible nucleotide bases (A or C). You model your system as an HMM (see figure below) where the nucleotide bases at each RNA location are the hidden variable (R) and the output by your system is the observed variable (Si). R R Rs S S2 S3 = 1 You can assume the following: • An RNA triplet is equally likely to start with either A or C; P(R1 = A) = P(R; = C) = 0.5. . there is a 25% chance that a nucleotide repeats itself (for example P(R2 = A|R= A) = 0.25). In general, P(Ri+1 = 2|R; = 2) = 0.25. • there is a 75% chance for correctly identifying a nucleotide (for example P(S1 = AR A) = 0.75). In general, P(S. = 3R = ) = 0.75. (a) (3 points) What is the joint probability of the model P(R1, R2, R3, S1, S2, S3) as the prod- uct of class conditional probabilities? (b) (3 points) Draw the lattice representation of the model. (c) (5 points) Given the output of the system as S = C, S, = A, S3 = A, label each of the probabilities for the edges in the lattice. (a) (7 points) Compute the probability of the second nucleotide base being given the above observation; P(R2 = A[S1 = C, S2 = A, S3 = A). You should use the forward-backward algorithm. (e) (2 points) You find out that there are actually four (4) possible nucleotide bases (A,C,U, and G). Given that at least 50 RNA triplets (like the one above) are required to represent a protein molecule. What will be the time taken by the algorithm in part (d) to compute a probability inference for an RNA sequence representing such a protein? You can assume that computing forward or backward value takes 1 second.