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Control parameter, $ \phi_{\tilde{w}}$

This is only required in model 3. $ \phi_{\tilde{w}}$ has a full conditional which can be sampled from. Hence for $ \phi_{\tilde{w}}$ we can employ Gibbs sampling. The full conditional for $ \phi_{\tilde{w}}$ is given by:
$\displaystyle \phi_{\tilde{w}}\vert.$ $\displaystyle \sim$ $\displaystyle Ga\left(
\frac{1}{4}\sum_i \su...
...\in{\cal N}_i}
\right)$ (28)

$ \tilde{a}_{\tilde{w}}$ is set to $ 10^{-4}$, and $ \tilde{b}_{\tilde{w}}$ is set to $ 10^{-4}$ to give a disperse prior.