$\lambda _{hi}$

This is sampled from using Metropolis-Hastings. We propose univariate jumps in the six parameter space of $\lambda _{hi}$ at each voxel. Metropolis-Hastings requires that the following terms are updated:

$$\prod_t p(q_{it}\vert\beta,\alpha,q_{i\tilde{t}<t},\phi_{\epsilon_i})$$ (48)

$$\prod_{t,j\in{\cal N} i} p(q_{jt}\vert\beta,\alpha,q_{i\tilde{t}<t},\phi_{\epsilon_j})$$ (49)

$$p(\lambda_{hi})$$ (50)