# Error propagation with non-linear least squares

How do you take the variance of the datapoints into account to compute variance estimates of the parameters of a non-linear least squares fit?

Suppose, I fit a non-linear model to a dataset $$\mathbf{d} = [d_k]$$, where each data point has a known variance $$\mathrm{Var}\, d_k$$. With the standard equation to compute the variance-covariance matrix, only the mean square error $$\mathrm{MSE}$$ and the Jacobian $$\mathbf{J}$$ are taken into account

$$\mathrm{Cov}\, p = \mathrm{MSE}\, \mathbf{J}^T \mathbf{J} .$$

The variance of the data points does not contribute. With weighted non-linear least squares, the relative weight of the datapoints is taken into account, but again, the variance of the parameters is independent of the "absolute" variance of the datapoints.

Am I missing something?