I would like to better understand the process that Mathematica uses to determine the standard error when fitting with NonlinearModelFit. I have been reading this post, which explains the code involved in the calculation. My current understanding is that the variable Eh is the precision matrix (a.k.a. concentration matrix) and that taking it's inverse gives the covariance matrix, whose diagonal elements represent the variance of each parameter. What I'm not understanding is how the elements of the precision matrix are related to the derivatives of logL that are calculated in h. Is that relationship generally true? Is it specific to the normal distribution? I have been combing through Google and Wikipedia for the last few hours, not making any headway. Any help or guidance would be greatly appreciated.

edit: JimB, thank you so much for your suggestion. I found this link, which answered my questions. And as for the terminology, I was only using the terms I found by digging through the Wikipedia articles on covariance.

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    $\begingroup$ Are "precision matrix" and "concentration matrix" physics terms/jargon? The standard statistics terms are "estimated information matrix" and "estimated Fisher information matrix". Looking up "mle estimated information matrix" will give you some informative links. $\endgroup$ – JimB Apr 13 '18 at 1:13
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    $\begingroup$ Ooops! Another gap in my statistical education. I have found the terms "precision matrix" (with the term "precision" which I do know is more likely used by Bayesians) and "concentration matrix" in Wikipedia as you stated. $\endgroup$ – JimB Apr 13 '18 at 15:00
  • $\begingroup$ In a sense, the whole business of calculating the Fisher information matrix amounts to fitting a Gaussian distribution to your distribution at the estimation point. This is really quite analogous to fitting a parabola to a local maximum of a function (since a Gaussian is just a parabola in log-space). $\endgroup$ – Sjoerd Smit Sep 26 '18 at 21:05

The OP mentioned in an edit to their question that a post on CrossValidated has the information they were looking for. Just for the sake of information recovery, and so that the question appears answered, I am adding the link below.

The post is:

Fisher Information matrix and relationship to Hessian and standard errors


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