Solution
= Solution
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.