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I need a covariance of parameter estimation for reliability estimation. According to the this post, I know the approximation of the Hessian can be calculated as

$$ \sigma^2 H^{-1} = C $$

where H is Hessian, C is the covariance and sigma is the variance of residual. I am trying to understand where it came from and how it is derived but I could not find a related material anywhere. Anyone knows a good reading material regarding this?

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The following two materials explain the problem clearly.

Why Hessian is same as covariance matrix. https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470824566.app1

How JtJ can be a Hessian approximation. https://www8.cs.umu.se/kurser/5DA001/HT07/lectures/lsq-handouts.pdf

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