Compute the joint evidence by one-dimensional numerical integration,
$$
\mathcal Z_{AB}=\int f_A(\theta)f_B(\theta)\pi(\theta)\,d\theta.
$$
Equivalently, the individual outputs give
$$
\mathcal Z_{AB}
=\mathcal Z_A\mathcal Z_B
\int\frac{\mathcal P_A(\theta)\mathcal P_B(\theta)}{\pi(\theta)}\,d\theta.
$$
Quadrature or one-dimensional <importance sampling> evaluates this integral without entering the $(\theta,\boldsymbol\alpha,\boldsymbol\beta)$ space.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-219/4/e/solution