$\epsilon$ and $\sigma$

A final problem is choosing appropriate values for $\sigma$ and $\epsilon$. Often we have a good idea of what our data variance is, but what we are actually adding random noise to is in the output space of our inverse noise covariance operator. How the variance in the data space translates to a variance in our noise covariance operator is far from obvious. In addition, if our $\sigma$ value is different from the variance of solving our estimation without noise added to the residual, we will need to modify our value of $\epsilon$ to achieve the same balance between our data fitting and model styling goal.