A Tutorial on Simplicity and Computational Differentiation for Statisticians

Authors: Stephen P. Smith

Automatic differentiation is a powerful collection of software tools that are invaluable in many areas including statistical computing. It is well known that automatic differentiation techniques can be applied directly by a programmer in a process called hand coding. However, the advantages of hand coding with certain applications are less appreciated, but these advantages are of paramount importance to statistics in particular. Based on the present literature, the variance component problem using restricted maximum likelihood is an example where hand coding derivatives was very useful relative to automatic or algebraic approaches. Some guidelines for hand coding backward derivatives are also provided, and emphasis is given to techniques for reducing space complexity and computing second derivatives.

Comments: 26 Pages.

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[v1] 2017-02-19 11:36:41

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