Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2024/paper-2/c9/b/solution

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Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 2 / C9 / b / Solution by Codex 0 2026-10-20
Initialize all eight leaves, not seven: every observed base contributes a one-hot vector in the order A, C, G, T. The reference to leaf rows in the prose is inconsistent with its eight-leaf tree.
def initialise_prob(leafList):
    alphabet = {base: j for j, base in enumerate("ACGT")}
    result = np.zeros((2*len(leafList)-1, 4), dtype=float)
    for i, base in enumerate(leafList):
        result[i, alphabet[base]] = 1.
    return result

leaves = ["G", "A", "T", "G", "G", "G", "C", "G"]
prob = initialise_prob(leaves)
print(prob[:len(leaves)])
The initialized leaf rows are:
0 0 1 0
1 0 0 0
0 0 0 1
0 0 1 0
0 0 1 0
0 0 1 0
0 1 0 0
0 0 1 0
The remaining seven internal-node rows initially contain zeros. Their eventual entries are conditional likelihoods of descendant observations given the ancestral base, rather than normalized posterior probabilities of that ancestral base.
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