...uncertainty

For the missing data problem $\epsilon$ could be used exclusively. As our data fitting goal becomes more complex, having a separate $\sigma$ and $\epsilon$ becomes useful.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.