 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2025/paper-1/6/b/solution

p^{a - 1} (1 - p)^{b - 1}

π (p ∣ x) \propto p^{a + n - 1} (1 - p)^{b + S - n - 1} .

This is again a beta distribution, namely

p ∣ x \sim Beta (a + n, b + S - n) .

Thus the beta family is a conjugate prior family for the geometric distribution. The update is an instance of beta-geometric conjugacy: counts of observed successes and failures are added to the two beta parameters.

 New to topics? Read the docs here!