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$ \phi _{\beta _{ij}}$ for ARD prior


$\displaystyle \phi_{\beta_{ij}}\vert.$ $\displaystyle \sim$ $\displaystyle Ga\left(\frac{1}{2}+\tilde{a}_{\beta},
\frac{\beta_{ij}^2}{2}+\tilde{b}_{\beta}\right)$ (36)