Background: LSQ

For data points $\{(x_i,y_i,\Delta y_i)\}_{i=1}^N$, the (weighted) least squares objective function (cf. Wikipedia) is

\[\text{lsq}(\lambda) = \sum_{i=1}^N \frac{(y_i - m(x_i,\lambda))^2}{\Delta y_i^2}\]

For the standard least squares objective function, one sets $Δy_i = 1$ for all $i = 1,\ldots,n$.

The optimal parameters $\lambda = \{\lambda_1,\ldots, \lambda_n\}$, given the data $\{(x_i,y_i,\Delta y_i)\}$ and the model function $m(x,\lambda)$, are those that minimize the least squares objective function $\text{lsq}(\lambda)$. An explanation for this statement can be found in Background:-Posterior-probability