Local Sensitivity Analysis Based on Derivative Approximations
This is the first of three successive chapters on the topic of sensitivity analysis, i.e., determining which variables a scalar quantity of interest depends on most strongly. Chapter explores using derivatives as local indicators of sensitivity based on finite difference approximations of first and second-order Taylor expansions. The error in the estimates due to finite differences is discussed, and the complex step approximation is offered as an approach for highly accurate derivative estimates for sensitivities of analytic functions. Second-order sensitivities are presented including both interactions between first-order sensitivities and second-derivative sensitivities.