Data Variability

As fitting goals (4) indicate, our fitting goals are in many ways symmetric. As a result, we should be able to replace the zero vector of our data fitting goal with another scaled random vector. We now have a second scaling factor $\sigma_{d}$ and a new set of fitting goals:

$$\begin{eqnarray} \sigma_{d} \bf \eta &\approx&\bf r_{d} = \bf N_{noise} ( \bf d-... ... \\ \sigma_{m} \bf \eta &\approx&\bf r_{m} = \epsilon \bf A\bf m .\end{eqnarray}$$ (9)

This new set of fitting goals offers the opportunity to see how the uncertainty in our data estimates affects our uncertainty in our model estimate. In the next section I will discuss some of the difficulties in making this formulation practical.