In typical quasi-Newton methods used for optimization problems, a matrix is derived to be a good approximation of the Hessian of the problem (the same is true for root finding problems with the Jacobian), and is used only within the algorithm to find a good descent direction.
In wikipedia, it was noted that this matrix can be used for "credible intervals or confidence intervals" estimation. However, there was not any citation for those uses. I couldn't find the adequate references for those uses.
I also noticed an article entitled "Randomized Quasi-Newton Updates are Linearly Convergent Matrix Inversion Algorithms" which showed how to use this matrix for inversion with a slightly enhanced BFGS algorithm.
I wanted to know if there were published works using the approximate Hessian matrix outside the quasi-Newton algorithm.