# Jacobian approximation at given point without explicit derivatives expression

after solving a NLproblem with optimization method, I would like to compute confidence intervals, prediction bounds and standard deviation for these optimal parameters. Explicit formulas I have read about do need computation of model derivatives with respect to parameters, taken at optimal parameters.

I wonder what available methods exist for such Jacobien computation.

I have an idea that methods like perturbation methods are quite suited, althought I cannot figure out what to use precisely as an algorithm. Or what to use as parameters for such a computation (Delta pertubation?).

Are there some existing recipes on this topic? Do you have good references to point to?

Thanks and regards.

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