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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-35/3/g/solution

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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 35 / 3 / g / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-06

With equal model prior probabilities, Bayes factor updating gives

w_{0} = B_{01} / (1 + B_{01})

and

w_{1} = 1/ (1 + B_{01})

. The Bayesian model averaging posterior density is therefore

p (β ∣ y) = \frac{B _{01}}{1 + B _{01}} p_{0} (β ∣ y) + \frac{1}{1 + B _{01}} p_{1} (β ∣ y) .

(1)

This is a two-component mixture model of the normal distributions already derived. For the numerical observation above, $w_{0} ≃ 0.10829$ and $w_{1} ≃ 0.89171$ . Consequently it is predominantly the wide-model posterior, not predominantly the narrow one.

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