An analysis of vectorised automatic differentiation for statistical applications

Abstract Automatic differentiation (AD) is a general method of computing exact derivatives in complex sensitivity analyses and optimisation routines in settings that lack closed-form solutions, thus posing challenges for analytical and numerical alternatives. This paper introduces a vectorised version of AD that builds on matrix calculus. This more transparent and efficient version of AD promotes its use in a wider range of statistical and econometric applications that require accurate and fast algorithms for the computation of derivatives when performing frequentist and Bayesian inferences. Numerical studies are presented to demonstrate the efficacy and speed of the proposed AD method compared with the numerical derivative scheme by exploiting, for example, sparse matrix representations and high-level optimisation techniques. JEL classifications: C11, C53, E37