Estimate each one-dimensional marginal posterior from its individual experiment's weighted samples, for example by weighted <kernel density estimation>. Combining that density estimate with the individual evidence estimate gives
$$
\widehat f_A(\theta)
=\frac{\widehat{\mathcal Z}_A\widehat{\mathcal P}_A(\theta)}{\pi(\theta)},
\qquad
\widehat f_B(\theta)
=\frac{\widehat{\mathcal Z}_B\widehat{\mathcal P}_B(\theta)}{\pi(\theta)}.
$$
Their product with $\pi(\theta)$ can be normalized on the one-dimensional $\theta$ space, avoiding all joint nuisance-parameter sampling.

Solution

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

 Solution

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