 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2021

Paper 219

It holds generally whenever the posterior is well defined and the expectations exist. Bayes' theorem gives
$$
\log\frac{p(\theta\mid y)}{\pi(\theta)}
=\log L(\theta)-\log Z.
$$
Taking posterior expectations yields
$$
D_{\mathrm{KL}}\{p(\theta\mid y)\Vert\pi\}
=\mathbb E_{\theta\mid y}\log L(\theta)-\log Z,
$$
which rearranges to the claimed evidence decomposition.


Solution

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

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

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

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

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)