I have a log likelihood function of a model and I want to find $\mu$ and $\sigma^2$ which maximize the log likelihood. Since the log lik function is quite complex, I decided to use Nelder-Mead algorithm from
scipy module. What I would like to do now is to estimate the errors on $\mu$ and $\sigma^2$ retrieved by Nelder-Mead algorithm.
How to do it without calculating the Hessian of the function?
EDIT: I found a way to approximate the Hessian (using numdifftools.core.Hessian) but I'm not sure how much can I rely on it.
EDIT 2: In some cases I manage to use the approximated Hessian (from
numdifftools) but in other cases, it doesn't work. And it seems like there is a number precision problem. So I'm still looking for a solution with which I can efficiently asses the approximation error without using Hessian or an implementation of a Hessian approximation which works good in high number precision.