 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

2019

Paper 207

For parameters $(\rho_G,\pi_1,\lambda)$ on $0<\rho_G<1$ and $(\pi_1,\lambda)\in\mathcal T$, conditional independence gives
$$
\begin{aligned}
\pi(\rho_G,\pi_1,\lambda\mid y_G,y_{S1},y_{S2})
\propto{}&
(\lambda\rho_G)^{y_G}(1-\lambda\rho_G)^{N-y_G}\\
&\times\pi_1^{y_{S1}}(1-\pi_1)^{n_{S1}-y_{S1}}\\
&\times(\pi_1+\lambda)^{y_{S2}}
(1-\pi_1-\lambda)^{n_{S2}-y_{S2}}\\
&\times\rho_G^{a-1}(1-\rho_G)^{b-1}
\mathbf1_{\mathcal T}(\pi_1,\lambda).
\end{aligned}
$$
This is the joint posterior up to its normalizing constant.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 1 / h / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 1 / h / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 1 / h / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)