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\begin{aligned} π (α, β | D) \propto {\begin{cases} L_{L H} (D | α, β) p (α, β) & if (α^{'}, β^{'})^{'} \sim MVN \\ L_{L H} (D | α, β) p (α) p (β) & otherwise \end{cases} \end{aligned}

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\begin{equation*} \begin{split} \pi (\balpha ,\bbeta |D) \propto \left\{ \begin{array}{ll} L_{\mr{LH}}(D|\balpha ,\bbeta ) p(\balpha ,\bbeta ) & \textrm{if } \quad (\balpha ',\bbeta ')' \sim \textrm{MVN} \\ L_{\mr{LH}}(D|\balpha ,\bbeta ) p(\balpha ) p(\bbeta ) & \textrm{otherwise} \end{array} \right. \end{split}\end{equation*}