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

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- Solution e

Solution

Compute the joint evidence by one-dimensional numerical integration,

Z_{A B} = \int f_{A} (θ) f_{B} (θ) π (θ) d θ .

Equivalently, the individual outputs give

Z_{A B} = Z_{A} Z_{B} \int \frac{P _{A} ( θ ) P _{B} ( θ )}{π ( θ )} d θ .

Quadrature or one-dimensional importance sampling evaluates this integral without entering the

(θ, α, β)

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