The <Kullback-Leibler divergence> between the posterior normal distribution and $N(0,\tau^2)$ is
$$
\boxed{
D_{\mathrm{KL}}\{p(\theta\mid y)\Vert\pi\}
=\frac12\left[
\frac{\sigma_\theta^2+\widetilde\theta^2}{\tau^2}
-1+\log\left(\frac{\tau^2}{\sigma_\theta^2}\right)
\right]}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 219 / 4 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-219/4/d/solution