AuxV2

(1)Sample ${({\kappa }_1^2)}^{(t+1)}$ from ${\mathcal{P}}_{{\kappa }_1^2|{\mathbf{x}}^{(t)},{\mathbf{\sigma }}^{(t)},{\beta }^{(t)},\mathbf{z}}$. (2)Sample ${({\kappa }_2^2)}^{(t+1)}$ from ${\mathcal{P}}_{{\kappa }_2^2|{\mathbf{x}}^{(t)},{\mathbf{\sigma }}^{(t)},{\beta }^{(t)},\mathbf{z}}$. (3)Sample ${\beta }^{(t+1)}$ from ${\mathcal{P}}_{\beta |{\mathbf{x}}^{(t)},{\mathbf{\sigma }}^{(t)},{({\kappa }_1^2)}^{(t+1)},{({\kappa }_2^2)}^{(t+1)}}$. (4)Sample ${\gamma }^{(t+1)}$ from ${\mathcal{P}}_{\gamma |{\mathbf{x}}^{(t)}}$. (5)Sample ${\mathbf{\sigma }}^{(t+1)}$ from ${\mathcal{P}}_{\mathbf{\sigma }|{\mathbf{x}}^{(t)},{\beta }^{(t+1)},{({\kappa }_1^2)}^{(t+1)},{({\kappa }_2^2)}^{(t+1)},\mathbf{z}}$. (6)Sample ${\mathbf{v}}_2^{(t+1)}$ from ${\mathcal{P}}_{{\mathbf{v}}_2|{\mathbf{x}}^{(t)}}$. (7)Set ${\mu }_1^{(t+1)}=ϵ{\parallel \mathbf{H}\parallel }_{\mathrm{S}}^{-2}min{\left({\sigma }_i^{(t+1)}\right)}_{1⩽i⩽N}^{-2}$ and sample ${\mathbf{v}}_1^{(t+1)}$ from ${\mathcal{P}}_{{\mathbf{v}}_1|{\mathbf{x}}^{(t)},{\mathbf{\sigma }}^{(t+1)}}$. (8)Sample ${\mathbf{x}}^{(t+1)}$ from ${\mathcal{P}}_{\mathbf{x}|{\mathbf{\sigma }}^{(t+1)},{\gamma }^{(t+1)},{\mathbf{v}}_1^{(t+1)},{\mathbf{v}}_2^{(t+1)},\mathbf{z}}$.