Solution
= Solution
The light-curve posterior used the analysis prior $\pi_0(\Delta t)=N(0,\sigma_{\mathrm{prior}}^2)$, so its marginal likelihood as a function of delay is proportional to $p(\Delta t\mid D)/\pi_0(\Delta t)$. Therefore
$$
p(H_0\mid D,M_l)\propto
\mathbf1_{[H_{0\min},H_{0\max}]}(H_0)
\int
\frac{p(\Delta t\mid D)}{\pi_0(\Delta t)}
p(\Delta t\mid H_0,M_l)\,d\Delta t.
$$
The integral can be evaluated numerically using the approximation from part (d).