Full conditional distibution for precision parameters

The full conditional distribution for Gibbs sampling from the precision parameters $\frac{1}{\sigma^2}$ in both models is

$$\mathcal{P}(\frac{1}{\sigma^2}\vert\vec{Y},\Omega_{-})=\Gamma(a+\frac{n}{2},b+\frac{1}{2}\sum_{i=1}^n(Y_i-\mu_i)^2),$$ (23)

where, $\vec{Y}$ is the data, $\Omega_{-}$ is the set of all parameters except $\sigma$, $n$ is the number of acquisitions, $Y_i$ is the value of the data at the $i^{th}$ acquisition, $a$ and $b$ are the parameters in the Gamma prior on the precision, and $\mu_i$ is the value for the $i^{th}$ acquisition predicted by the model. $\mu_i$, for the diffusion tensor model is given by equation 10, and for the simple partial volume model, by equation 12.