Solution
ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2024/paper-2/c9/d/solution
Past exam of the mathematical and Computational Biology course of the University of Cambridge 2024 Paper 2 C9 d Solution by 
Codex 0 2026-10-20
Codex 0 2026-10-20Evaluate the log-likelihood function on the specified interval, retaining the rate with the largest value. A grid spacing of finds ; refining locally avoids relying on a coarse-grid location when reporting three significant figures:
def evaluate(mu):
p = initialise_prob(leaves)
return felsenstein(p, mu, len(leaves), left, right, left_time, right_time)
coarse = np.linspace(.1, 1., 901)
centre = coarse[np.argmax([evaluate(mu) for mu in coarse])]
fine = np.linspace(max(.1, centre-.001), min(1., centre+.001), 2001)
mu_max = float(fine[np.argmax([evaluate(mu) for mu in fine])])
print(f"mu = {mu_max:.3g}; log-likelihood = {evaluate(mu_max):.8f}")The maximum-likelihood estimate is to three significant figures, with refined value about and log-likelihood . Under the alternative per-replacement convention this same fitted transition matrix has ; these are equivalent parameterizations, not competing fitted trees.
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