Derivative-based uncertainty quantification: automatic differentiation tools for SAS

Abstract

Automatic differentiation, or more properly algorithmic differentiation (AD), is a technique for efficiently computing accurate derivatives for numerical models. It is based on augmenting the code with partial derivatives of elementary mathematical operations on important variables and retracing the calculation flow (in forward or reverse direction) to assemble derivatives by chain rule. The relative computational overhead associated with AD is bounded, independent of dimension, and is largely independent of the mathematical model.