AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

David A. Fournier, Hans J. Skaug, Johnoel Ancheta, Jim Ianelli, Arni Magnusson, Mark Maunder, Anders Nielsen, John Sibert

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Abstract

Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages ofADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty
Original languageEnglish
JournalOptimization Methods and Software
Volume27
Issue number2
Pages (from-to)233-249
ISSN1055-6788
DOIs
Publication statusPublished - 2011

Cite this

Fournier, David A. ; Skaug, Hans J. ; Ancheta, Johnoel ; Ianelli, Jim ; Magnusson, Arni ; Maunder, Mark ; Nielsen, Anders ; Sibert, John. / AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. In: Optimization Methods and Software. 2011 ; Vol. 27, No. 2. pp. 233-249.
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AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. / Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel; Ianelli, Jim; Magnusson, Arni; Maunder, Mark; Nielsen, Anders; Sibert, John.

In: Optimization Methods and Software, Vol. 27, No. 2, 2011, p. 233-249.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Fournier, David A.

AU - Skaug, Hans J.

AU - Ancheta, Johnoel

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AU - Magnusson, Arni

AU - Maunder, Mark

AU - Nielsen, Anders

AU - Sibert, John

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AB - Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages ofADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty

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