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$ \phi _{\alpha _p}$ for MRF prior


$\displaystyle \phi_{\alpha}\vert.$ $\displaystyle \sim$ $\displaystyle G\left(
\frac{N}{2}+\tilde{a}_{\alpha},
\frac{1}{4}\sum_i \sum_{j\in{\cal N}_{i}}\left(
(\alpha_{pi}-\alpha_{pj})^2\right)
\right.$  
    $\displaystyle \left.
+\tilde{b}_{\alpha}
\right)$ (47)