Application of automatic differentiation in modern nonlinear regression
by
Mark Huiskes
Wageningen University

In traditional nonlinear regression, model parameters are estimated by means of maximization of a likelihood function, usually assuming a normal error structure. Subsequently, parameter uncertainty information is obtained by linearization of the model around the parameter estimate.

Recently methods have been developed that extend this approach using higher-order derivatives. This presentation will have three aims: (i) to provide an overview of these methods; (ii) to discuss the role of automatic differentiation in these methods; (iii) to discuss the requirements of these methods with respect to the design of automatic differentiation routines.

The described methods have been implemented by the author in a C++ library, named MAP. The library is aimed at the analysis of models represented by smooth maps and uses ADOL-C for the automatic differentiation.

Extended abstract

Date received: January 26, 2000