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

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- Solution b

Solution

Independence of the experiments gives

P_{A B} (θ, α, β) = \frac{L _{A} ( θ , α ) L _{B} ( θ , β ) π ( θ ) π ( α ) π ( β )}{Z _{A B}},

where

Z_{A B} = ∭ L_{A} L_{B} π (θ) π (α) π (β) d θ d α d β .

The marginal posterior is obtained by integrating the displayed joint posterior over both nuisance-parameter vectors.

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