Algorithm 2.

Block Gibbs sampler for $\mathrm{\Omega }~\mathrm{\pi }(\mathrm{\Omega }|{\mathbb{X}}_{\mathrm{n}},\mathrm{\Lambda })$.

Input: $S={\sum }_{r=1}^n{\left(X^{(r)}-\overline{X}\right)}^{\prime }\left(X^{(r)}-\overline{X}\right)$ and Λ; start value of Ω; number of iterations B.

For b =1,..., B :

1. For i < j: sample ${\tau }_{ij}^{-1}~\mathrm{Inv}\text{Gaussian}({({\lambda }_{ij}|{\omega }_{ij}|)}^{-1},2)$.

2. For i = 1, ...,d: compute ${\Omega }_{-ii}={\Omega }_{i-i}^{\prime }≔\eta$ and

${\omega }_{ii}:=\xi +{\eta }^{\prime }{\Omega }_{-i-i}^{-1}\eta$, where

ξ ~ Γ(n/2 + 1, Sii/2 + λii), and η ~ N(−AS−ii,A), with

$A={\left[\left(S_{ii}+2{\lambda }_{ii}\right){\Omega }_{-i-i}^{-1}+D\right]}^{-1}$ and

$D=2\mathrm{diag}\left(\frac{{\lambda }_{1i}^2}{{\tau }_{1i}},\dots ,\frac{{\lambda }_{(i-1)i}^2}{{\tau }_{(i-1)i}},\frac{{\lambda }_{(i+1)1}^2}{{\tau }_{(i+1)i}},\dots ,\frac{{\lambda }_{di}^2}{{\tau }_{di}}\right)$.

3. Set Ω(b) = Ω.

Output: Sequence Ω(1),..., Ω(B).