Finite Difference Method variance equation

It is assumed that the objective function is known only implicitly so the finite difference method is used to estimate the Hessian and, hence, the variance of this random variable. By Equation (A.5), the Hessian can be evaluated at an arbitrary point 9 ... 

For a random variable with a small uncertainty, the variance can be approximated by To demonstrate this, let a = ii/ for Equation (A.ll) so the mean is jx and the variance is /u/3. For small /3, the Hessian estimated by finite difference method can be approximated by ... 

Equation 4.61 may be used to calculate the integral (4.50) to derive the volume effect. Again, the integral may be solved using the finite differences method. Results are shown in Rg. 4.31 by the solid line. Dashed line, instead, indicates the volume effect evaluated using m — 40 constant. This time, at variance with the DCI calculations, there is no significant difference between the two calculations. 

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