The simulation catalog is a sample from the joint prior. <Self-normalized importance sampling> therefore estimates the posterior mean by
$$
\overline m_w=\sum_{i=1}^Km_iw_i,
\qquad
w_i=\frac{p(d\mid x_i)}{\sum_{j=1}^Kp(d\mid x_j)}.
$$
The likelihood weights update each simulated system according to how well its satellite resembles the measured one.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 219 / 2 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-219/2/b/solution