AD model builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. 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 of ADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Itzá Balam, Reymundo; Hernandez-Lopez, Francisco; Trejo-Sánchez, Joel; Uh Zapata, Miguel: An immersed boundary neural network for solving elliptic equations with singular forces on arbitrary domains (2021)
  2. Signorelli, Mirko; Spitali, Pietro; Tsonaka, Roula: Poisson-Tweedie mixed-effects model: a flexible approach for the analysis of longitudinal RNA-seq data (2021)
  3. Zheng, Nan; Cadigan, Noel: Frequentist delta-variance approximations with mixed-effects models and TMB (2021)
  4. Mohamed, Shakir; Rosca, Mihaela; Figurnov, Michael; Mnih, Andriy: Monte Carlo gradient estimation in machine learning (2020)
  5. Olsen, Christian Haargaard; Ottesen, Johnny T.; Smith, Ralph C.; Olufsen, Mette S.: Parameter subset selection techniques for problems in mathematical biology (2019)
  6. Kulshreshtha, K.; Narayanan, S. H. K.; Bessac, J.; MacIntyre, K.: Efficient computation of derivatives for solving optimization problems in R and Python using SWIG-generated interfaces to ADOL-C (2018)
  7. Patterson, Toby A.; Parton, Alison; Langrock, Roland; Blackwell, Paul G.; Thomas, Len; King, Ruth: Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges (2017)
  8. Wang, S.; Cadigan, N. G.; Benoît, H. P.: Inference about regression parameters using highly stratified survey count data with over-dispersion and repeated measurements (2017)
  9. Asar, Özgür; Ritchie, James; Kalra, Philip A.; Diggle, Peter J.: Short-term and long-term effects of acute kidney injury in chronic kidney disease patients: a longitudinal analysis (2016)
  10. Huang, Lu; Tang, Li; Zhang, Bo; Zhang, Zhiwei; Zhang, Hui: Comparison of different computational implementations on fitting generalized linear mixed-effects models for repeated count measures (2016)
  11. Kasper Kristensen and Anders Nielsen and Casper Berg and Hans Skaug and Bradley Bell: TMB: Automatic Differentiation and Laplace Approximation (2016) not zbMATH
  12. Perry de Valpine; Daniel Turek; Christopher J. Paciorek; Clifford Anderson-Bergman; Duncan Temple Lang; Rastislav Bodik: Programming with models: writing statistical algorithms for general model structures with NIMBLE (2015) arXiv
  13. Xu, Ximing; Cantoni, Eva; Flemming, Joanna Mills; Field, Chris: Robust state space models for estimating fish stock maturities (2015)
  14. Skaug, Hans J.; Yu, Jun: A flexible and automated likelihood based framework for inference in stochastic volatility models (2014)
  15. Cattelan, Manuela; Varin, Cristiano: Hybrid pairwise likelihood analysis of animal behavior experiments (2013)
  16. Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel; Ianelli, James; Magnusson, Arni; Maunder, Mark N.; Nielsen, Anders; Sibert, John: AD model builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models (2012)
  17. Millar, Russell B.: Maximum likelihood estimation and inference. With examples in R, SAS and ADMB (2011)