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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-219/3/f/solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 219 / 3 / f / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

With equal model prior probabilities, Bayesian model averaging gives the unnormalized density

p (H_{0} ∣ D) \propto 1_{[H_{0 m i n}, H_{0 m a x}]} (H_{0}) \frac{1}{m} \sum_{l = 1}^{m} \int \frac{p ( Δ t ∣ D )}{π _{0} ( Δ t )} p (Δ t ∣ H_{0}, M_{l}) d Δ t .

(1)

Normalizing this expression over the allowed interval automatically incorporates each lens model's evidence and hence its posterior model probability.

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