I am confused about calculating errors. I have learned if you take the variance covariance matrix [itex]\Sigma_{ij}[/itex] of a fit of function f(x,p) to data for parameters [itex]p_i[/itex] (for example by using Levenberg-Marquart) that the one sigma error interval for [itex]p_i[/itex] is [tex]\sigma_{p_i}=\sqrt{\Sigma_{ii}}[/tex] I only understand this, if there are no covariance terms. Why do we do this? I would have thought a better way to find the error would be to do diagonalize [itex]\Sigma[/itex], say the diagonal form is [itex]\Xi[/itex] with normalized eigenvectors [itex](\vec{v})_k[/itex]. Then we would have independent variables that have a Gaussian distribution and one can calculate the error on [itex]p_i[/itex] using error propagation, i.e. [tex]\sigma_{p_i} = \sqrt{\sum \Xi_{kk}\left\langle(\vec{v})_k\mid l_i \right\rangle}[/tex] where [itex]\left\langle(\vec{v})_k\mid l_i \right\rangle[/itex] is the [itex]i^\text{th}[/itex] component of [itex](\vec{v})_k[/itex]. If this is permissible, is there a name for it?(adsbygoogle = window.adsbygoogle || []).push({});

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# Error Propagation

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