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Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 219 / 4 / c / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 219 4 c
Created 2026-09-24 Updated 2026-09-25  0 By others on same topic  0 Discussions Create my own version
Define the prior-predictive nuisance integrals
fA​(θ)=∫LA​(θ,α)π(α)dα,fB​(θ)=∫LB​(θ,β)π(β)dβ.
(1)
Then
PAB​(θ)ZAB​=fA​(θ)fB​(θ)π(θ).
(2)
For each individual analysis, Bayes theorem also gives
fA​(θ)=π(θ)ZA​PA​(θ)​,fB​(θ)=π(θ)ZB​PB​(θ)​.
(3)

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