Suppose I have a variance-covariance matrix for three (log) parameters $$ \text{Var}\left[\left(\log\theta, \log \phi, \log \psi\right)\right] = \begin{pmatrix} \Sigma_{11} & \Sigma_{12} & \Sigma_{13} \\ \Sigma_{21} & \Sigma_{22} & \Sigma_{23} \\ \Sigma_{31} & \Sigma_{32} & \Sigma_{33}\end{pmatrix} $$ How do I find the standard deviations for $\theta$, $\phi$ and $\psi$? I can see two ways of finding it, but they give different results
- $\exp\left(\sqrt{\Sigma_{ii}}\right)$
- $\sqrt{\exp\left(\Sigma_{ii}\right)}$
which one is correct and why?